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A265836
Expansion of Product_{k>=1} 1/(1 - k*(k+1)*x^k).
3
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
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 16 2015
STATUS
approved