A325949 a(n) = 4^n * [x^n] sqrt(1-x) * Product_{k>=1} (1 + x^k).

1, 2, 6, 84, 198, 1660, 8348, 38632, 172358, 1015020, 4815796, 21693720, 112008732, 512079960, 2529630072, 12483215056, 56441387078, 264961478476, 1310206109508, 5906484485688, 28063437172276, 133423036122888, 611266244837128, 2826358342342832

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

a(n) ~ sqrt(Pi/3) * exp(Pi*sqrt(n/3)) * 2^(2*n - 5/2) / n.

a(n) = A325950(n) - 4*A325950(n-1).

Mathematica

nmax = 30; CoefficientList[Series[(1-x)^(1/2) * Product[(1+x^k), {k, 1, nmax}], {x, 0, nmax}], x] * 4^Range[0, nmax]
Table[4^n*(PartitionsQ[n] - Sum[PartitionsQ[n-k]*CatalanNumber[k - 1]/2^(2*k - 1), {k, 1, n}]), {n, 0, 30}]

Crossrefs

Cf. A000009, A325948, A325950.

Sequence in context: A352313 A357028 A245463 * A055706 A370984 A118537

Adjacent sequences: A325946 A325947 A325948 * A325950 A325951 A325952

Keyword

nonn

Author

Vaclav Kotesovec, May 28 2019

Status

approved