A215911 G.f.: exp( Sum_{n>=1} A215910(n)*x^n/n ), where A215910(n) equals the sum of the n-th power of multinomial coefficients in row n of triangle A036038.

1, 1, 3, 84, 88602, 5137769389, 23588076629522583, 11893878960703225919597767, 876545054865944028047877165082786426, 12147135901759930712215268630715086378214795245696, 39632791164678725520866813137932593902239710762044280903318659253

Offset: 0

Author

Paul D. Hanna, Aug 26 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 84*x^3 + 88602*x^4 + 5137769389*x^5 +...
such that the logarithm of the g.f. begins:
log(A(x)) = x + 5*x^2/2 + 244*x^3/3 + 354065*x^4/4 + 25688403126*x^5/5 + 141528428949437282*x^6/6 +...+ A215910(n)*x^n/n +...
where the coefficients A215910(n) begin:
A215910(1) = 1^1 = 1;
A215910(2) = 1^2 + 2^2 = 5;
A215910(3) = 1^3 + 3^3 + 6^3 = 244;
A215910(4) = 1^4 + 4^4 + 6^4 + 12^4 + 24^4 = 354065;
A215910(5) = 1^5 + 5^5 + 10^5 + 20^5 + 30^5 + 60^5 + 120^5 = 25688403126; ...
and equal the sums of the n-th power of multinomial coefficients in row n of triangle A036038.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A215910, A183239, A183241, A183241, A182963.

Programs

PARI

{a(n)=local(L=sum(m=1,n,m!^m*polcoeff(1/prod(k=1, n, 1-x^k/k!^m +x*O(x^m)), m)*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}
for(n=0,15,print1(a(n),", "))

Formula

a(n) ~ (n!)^n / n. - Vaclav Kotesovec, Feb 19 2015

a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2 - 1) / exp(n^2 - 1/12). - Vaclav Kotesovec, Feb 19 2015