A350642 Expansion of Product_{k>=1} (1-q^(2*k))/(1-q^k)^4.

1, 4, 13, 36, 90, 208, 455, 948, 1901, 3688, 6955, 12792, 23019, 40612, 70395, 120072, 201822, 334684, 548158, 887500, 1421602, 2254460, 3541928, 5515900, 8519173, 13055208, 19859113, 29998024, 45012751, 67116436, 99472320, 146580028, 214811311, 313149460

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

George E. Andrews and Peter Paule, MacMahon's partition analysis XIII: Schmidt type partitions and modular forms, Journal of Number Theory Available online 22 October 2021. See 4.1 p. 8.

Mathematica

m = 50; CoefficientList[Series[Product[(1 - q^(2*k))/(1 - q^k)^4, {k, 1, m}], {q, 0, m}], q] (* Amiram Eldar, Jan 09 2022 *)

Prog

(PARI) lista(nn) = my(q='q+O('q^nn)); Vec(prod(k=1, nn, (1-q^(2*k))/(1-q^k)^4));

Crossrefs

Cf. A350643, A350644.

Sequence in context: A320589 A328542 A036629 * A079922 A053563 A221882

Adjacent sequences: A350639 A350640 A350641 * A350643 A350644 A350645

Keyword

nonn

Author

Michel Marcus, Jan 09 2022

Status

approved