OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..30
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
EXAMPLE
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.
PROG
(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), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 26 2012
STATUS
approved