A265836 Expansion of Product_{k>=1} 1/(1 - k*(k+1)*x^k).

1, 2, 10, 32, 120, 342, 1206, 3320, 10604, 29578, 88342, 239400, 702020, 1863654, 5262650, 13948824, 38427192, 100244162, 272822282, 703972024, 1883948848, 4839944150, 12779850278, 32548367784, 85335644100, 215826029018, 560407835934, 1412632075328

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

Formula

a(n) ~ c * 6^(n/2), where

c = 79.0418032646837469192452349...... if n is even,

c = 78.4480460169710091436913691...... if n is odd.

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1,
      2^n, b(n, i-1)+(1+i)*i*b(n-i, min(n-i, i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..33);  # Alois P. Heinz, Aug 16 2019

Mathematica

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

Crossrefs

Cf. A074141, A077335, A092485, A305204.

Sequence in context: A367704 A034555 A084154 * A083099 A032095 A328039

Adjacent sequences: A265833 A265834 A265835 * A265837 A265838 A265839

Keyword

nonn

Author

Vaclav Kotesovec, Dec 16 2015

Status

approved