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To do so, we transform our series to series of the type $$\\sum_{n=0}^\\infty\\frac{an+b}{m^n}\\sum_{k=0}^n\\binom nk^4$$ studied by Cooper in 2012. In addition, we pose $17$ new series for $1/\\pi$ motivated by congruences; for example, we conjecture that $$\\sum_{k=0}^\\infty\\frac{4290k+367}{3136^k}\\binom{2k}kT_k(14,1)T_k("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2009.04379","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-09-09T15:58:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"25319e76bd89205f0822d323ffa7b29de93522544e1e151f094b025fd45fa3ac","abstract_canon_sha256":"0e7420c675abb2f57e85027059e9204169a0f4e0a011193c32a504fce93b0bb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:44:36.540961Z","signature_b64":"Wm8OGqSTUdBZfcN9MsmRiv+TTznVWHmfVucVyG9HrndltHNVqu6b38Mm28/wv36t6tdUEivGLZsuwiVKr5BWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a535da112856ebfa692eea21a101b735976e7867a1bf8c3163ad002db71d64cf","last_reissued_at":"2026-07-05T05:44:36.540462Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:44:36.540462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some new series for $1/\\pi$ motivated by congruences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Zhi-Wei Sun","submitted_at":"2020-09-09T15:58:08Z","abstract_excerpt":"In this paper, we deduce a family of six new series for $1/\\pi$; for example, $$\\sum_{n=0}^\\infty\\frac{41673840n+4777111}{5780^n}W_n\\left(\\frac{1444}{1445}\\right) =\\frac{147758475}{\\sqrt{95}\\,\\pi}$$ where $W_n(x)=\\sum_{k=0}^n\\binom nk\\binom{n+k}k\\binom{2k}k\\binom{2(n-k)}{n-k}x^k$. To do so, we transform our series to series of the type $$\\sum_{n=0}^\\infty\\frac{an+b}{m^n}\\sum_{k=0}^n\\binom nk^4$$ studied by Cooper in 2012. 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