A265974 Expansion of Product_{k>=1} 1/(1 - 3*k*x^k).

1, 3, 15, 54, 210, 699, 2484, 7995, 26610, 84186, 269940, 839238, 2634579, 8098194, 25032282, 76388265, 233791104, 709501596, 2157488730, 6523204836, 19747491810, 59558682132, 179762506329, 541222906812, 1630300772106, 4902697929306, 14748249476553

Offset

0,2

Links

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

Formula

a(n) ~ c * 3^n, where c = Product_{m>=2} 1/(1 - m/3^(m-1)) = 5.86277744540963226378877460838259757442241952947887939654316926419876...

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1,
      3^n, b(n, i-1) +i*3*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/(1-3*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A006906, A265951, A265975, A265976.

Cf. A246935, A242587.

Sequence in context: A286986 A261565 A085480 * A099581 A026696 A082708

Adjacent sequences: A265971 A265972 A265973 * A265975 A265976 A265977

Keyword

nonn

Author

Vaclav Kotesovec, Dec 19 2015

Status

approved