A336767 The number of partitions of n into an even number of parts, each part occurring at most seven times, minus the number of partitions of n into an odd number of parts, each part occurring at most seven times.

1, -1, 0, -1, 1, -1, 1, -1, 1, -1, 2, -1, 2, -2, 2, -3, 2, -2, 3, -3, 3, -4, 4, -4, 4, -5, 5, -6, 6, -6, 7, -7, 7, -8, 9, -9, 10, -10, 11, -12, 13, -13, 14, -15, 15, -17, 18, -18, 20, -21, 22, -23, 24, -25, 27, -29, 30, -32, 33, -35, 37, -39, 40, -43, 45, -47, 50

Offset: 0

Author

Jeremy Lovejoy, Aug 04 2020

Keywords

• sign

Links

• H. L. Alder and A. A. Muwafi, Identities relating the number of partitions into an even and odd number of parts, Fibonacci Quarterly, 13 (1975), 147-149.

Crossrefs

Cf. A000041, A106459, A261775, A336766.

Formula

G.f.: Product_{n>0} ((1-q^(8*n))/(1+q^n)).