A265975 Expansion of Product_{k>=1} 1/(1 - 4*k*x^k).

1, 4, 24, 108, 512, 2164, 9464, 39004, 163008, 663588, 2713752, 10954764, 44328512, 178160724, 716821752, 2874497660, 11532111232, 46187508676, 185028540696, 740595436652, 2964628293504, 11862432443764, 47467812675320, 189902835709212, 759756868215872

Offset: 0

Author

Vaclav Kotesovec, Dec 19 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A006906, A265951, A265974, A265976.

Cf. A246935, A246936.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1,
      4^n, b(n, i-1) +i*4*b(n-i, min(n-i, i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..32);  # Alois P. Heinz, Aug 23 2019

Mathematica

nmax=40; CoefficientList[Series[Product[1/(1-4*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 4^n, where c = Product_{m>=2} 1/(1 - m/4^(m-1)) = 2.700170514502619666262858845683166558216386190684736249639219328278569...