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A297322
a(n) = [x^n] Product_{k>=1} (1 + k*x^k)^n.
7
1, 1, 5, 28, 137, 726, 3896, 21071, 115089, 633007, 3500740, 19448573, 108458924, 606787572, 3404112479, 19142919543, 107874784017, 609021410570, 3443952349385, 19503777943838, 110599636109572, 627924447630011, 3568885868192419, 20304321490356084
OFFSET
0,3
LINKS
FORMULA
a(n) = A297321(n,n).
a(n) ~ c * d^n / sqrt(n), where d = 5.814548482877687529318372516965305077397562... and c = 0.2563102401728134539247148322678842806264... - Vaclav Kotesovec, Aug 01 2019
MAPLE
f:= proc(n) local k;
coeff(series(mul((1+k*x^k)^n, k=1..n), x, n+1), x, n);
end proc:
map(f, [$0..30]); # Robert Israel, Dec 28 2017
MATHEMATICA
Table[SeriesCoefficient[Product[(1 + k x^k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 24}]
CROSSREFS
Main diagonal of A297321.
Sequence in context: A258628 A054148 A272319 * A037591 A270922 A037682
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 28 2017
STATUS
approved