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A309652
a(n) = [x^n] B(x)^n, where B(x) is g.f. of A000312.
3
1, 1, 9, 106, 1493, 24276, 448122, 9301251, 215547845, 5541171496, 156997349684, 4870353700532, 164366482285898, 5998207807965543, 235388194276592723, 9884482616014596546, 442206843338189113445, 20995082225203329126384, 1054247070579064423466016
OFFSET
0,3
LINKS
FORMULA
a(n) ~ exp(exp(-1)) * n^(n+1).
MAPLE
B:= proc(n) option remember; n^n end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, B(n),
(h-> add(b(j, h)*b(n-j, i-h), j=0..n))(iquo(i, 2))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..20); # Alois P. Heinz, Aug 23 2019
MATHEMATICA
Table[SeriesCoefficient[(1+Sum[k^k*x^k, {k, 1, n}])^n, {x, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 11 2019
STATUS
approved