For every ν≥0 the partition function p(n) satisfies a pentagonal-number recurrence involving a divisor sum and a weight 2ν Hecke trace; ν=0 recovers Euler's recurrence.
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Pentagonal number recurrence relations for $p(n)$
For every ν≥0 the partition function p(n) satisfies a pentagonal-number recurrence involving a divisor sum and a weight 2ν Hecke trace; ν=0 recovers Euler's recurrence.