A325948 a(n) = 4^n * [x^n] sqrt(1-x) * Product_{k>=1} 1/(1 - x^k).

1, 2, 22, 116, 806, 4028, 26876, 132776, 808710, 4170604, 23586836, 120316888, 673359196, 3383189976, 18228019512, 92654842960, 486382544838, 2443171359820, 12694346947492, 63262412763896, 323739858349684, 1609270321201800, 8117702067063368, 40102791350319408

Offset

0,2

Links

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

Formula

a(n) ~ sqrt(Pi) * exp(Pi*sqrt(2*n/3)) * 2^(2*n - 9/4) / (3^(3/4) * n^(5/4)).

a(n) = A325947(n) - 4*A325947(n-1).

Mathematica

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

Crossrefs

Cf. A000041, A325947, A325949.

Sequence in context: A344498 A281140 A105237 * A216801 A083833 A221697

Adjacent sequences: A325945 A325946 A325947 * A325949 A325950 A325951

Keyword

nonn

Author

Vaclav Kotesovec, May 28 2019

Status

approved