A293864 - OEIS

%I #6 Oct 18 2017 17:16:53

%S 1,1,2,42,2472,295320,61369920,20250513360,9970976453760,

%T 6994020967113600,6738118625057702400,8654627604114610272000,

%U 14457770976132703296000000,30761772133454776218220416000,81885712959925376996901780172800,268520193454950330194198952198144000

%N a(0) = a(1) = 1; a(n) = n! * [x^n] (Sum_{k=0..n-1} a(k)*x^k/k!)^n.

%H Vaclav Kotesovec, <a href="/A293864/b293864.txt">Table of n, a(n) for n = 0..180</a>

%F From _Vaclav Kotesovec_, Oct 18 2017: (Start)

%F a(n) ~ c * n!^3/sqrt(n), where c = 0.500612869985729164508780668394780439268735...

%F a(n) ~ c * n^(3*n+1)/exp(3*n), where c = 7.884457436083884678947729926892032034...

%F (End)

%e 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! + ...

%t 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}]

%Y Cf. A000142, A001813, A177752, A293860.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Oct 18 2017