A206830 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, n*k) * x^k ).

1, 1, 2, 5, 34, 520, 14397, 993806, 222547738, 98753510701, 66772601607218, 82150206439975648, 310163020349941301606, 3022167582612808506550780, 47176617497043375266215814522, 1129578055293824008530028604347686, 62478430488069985838347598494293429802

Offset: 0

Author

Paul D. Hanna, Feb 12 2012

Keywords

• nonn

Comments

Note: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n^2} binomial(n^2, k) * x^k ) does not yield an integer series (see A227467).

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 34*x^4 + 520*x^5 + 14397*x^6 + ...
such that, by definition, the logarithm equals:
log(A(x)) = x*(1+x) + x^2*(1 + 6*x + x^2)/2 + x^3*(1 + 84*x + 84*x^2 + x^3)/3 + x^4*(1 + 1820*x + 12870*x^2 + 1820*x^3 + x^4)/4 + x^5*(1 + 53130*x + 3268760*x^2 + 3268760*x^3 + 53130*x^4 + x^5)/5 + ... + x^n/n*Sum_{k=0..n} A209330(n,k)*x^k + ...
More explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 115*x^4/4 + 2416*x^5/5 + 83064*x^6/6 + ...
		

Crossrefs

Cf. A167006, A201556, A227467, A209330, A207137, A228905.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m^2, m*k)*x^k)*x^m/m)+x*O(x^n)), n)}
for(n=0,15,print1(a(n),", "))