A293864 a(0) = a(1) = 1; a(n) = n! * [x^n] (Sum_{k=0..n-1} a(k)*x^k/k!)^n.

1, 1, 2, 42, 2472, 295320, 61369920, 20250513360, 9970976453760, 6994020967113600, 6738118625057702400, 8654627604114610272000, 14457770976132703296000000, 30761772133454776218220416000, 81885712959925376996901780172800, 268520193454950330194198952198144000

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

Cf. A000142, A001813, A177752, A293860.

Sequence in context: A235776 A216336 A152286 * A208297 A278150 A193271

Adjacent sequences: A293861 A293862 A293863 * A293865 A293866 A293867

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 18 2017

Status

approved