A325947 a(n) = 4^n * [x^n] 1/sqrt(1-x) * Product_{k>=1} 1/(1 - x^k).

1, 6, 46, 300, 2006, 12052, 75084, 433112, 2541158, 14335236, 80927780, 444028008, 2449471228, 13181074888, 70952319064, 376464119216, 1992239021702, 10412127446628, 54342856734004, 280633839699912, 1446275217149332, 7394371189799128, 37695186826259880

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) * 2^(2*n - 7/4) / (sqrt(Pi) * 3^(1/4) * n^(3/4)).

a(n) = Sum_{j=0..n} A325948(j)*4^(n-j).

Mathematica

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

Crossrefs

Cf. A000041, A325948, A325950.

Sequence in context: A327935 A079910 A103768 * A240779 A073507 A155598

Adjacent sequences: A325944 A325945 A325946 * A325948 A325949 A325950

Keyword

nonn

Author

Vaclav Kotesovec, May 28 2019

Status

approved