OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..180
FORMULA
From Vaclav Kotesovec, Oct 18 2017: (Start)
a(n) ~ c * n!^3/sqrt(n), where c = 0.500612869985729164508780668394780439268735...
a(n) ~ c * n^(3*n+1)/exp(3*n), where c = 7.884457436083884678947729926892032034...
(End)
EXAMPLE
E.g.f. A(x) = 1 + x + 2*x^2/2! + 42*x^3/3! + 2472*x^4/4! + 295320*x^5/5! + 61369920*x^6/6! + ...
MATHEMATICA
a[n_] := a[n] = n! SeriesCoefficient[Sum[a[k] x^k/k!, {k, 0, n - 1}]^n, {x, 0, n}]; a[0] = 1; a[1] = 1; Table[a[n], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 18 2017
STATUS
approved