A265976 Expansion of Product_{k>=1} 1/(1 - 5*k*x^k).

1, 5, 35, 190, 1070, 5525, 29080, 147485, 752790, 3789170, 19105800, 95794930, 480650335, 2406018490, 12047084370, 60264282575, 301493182380, 1507758356660, 7540528037090, 37705593514220, 188545393000350, 942756783659980, 4713958620697385, 23570092258449540

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, A265975.

Cf. A246935, A246937.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1,
      5^n, b(n, i-1) +i*5*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/(1-5*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 5^n, where c = Product_{m>=2} 1/(1 - m/5^(m-1)) = 1.977268427518901757865749340705853730491796767544158844539130847296...