A156630 G.f.: A(x) = Sum_{n>=0} [ Sum_{k>=1} (2^n + 2^k)^k*x^k/k ]^n / n!, a power series in x with integer coefficients.

1, 4, 36, 692, 38186, 10012732, 14013453284, 89892733239928, 2455110210935634790, 278266942487534934333100, 129264916198375365693754194988, 244287539590735476133066282560012360

Offset: 0

Author

Paul D. Hanna, Feb 12 2009

Keywords

• nonn

Comments

Compare to these dual g.f.s:

Sum_{n>=0} [ Sum_{k>=1} (2^n+1)^k*x^k/k ]^n/n! (A133991);

Sum_{n>=0} [ Sum_{k>=1} (2^k+1)^k*x^k/k ]^n/n! (A155201);

which, when expanded as power series in x, have only integer coefficients.

Examples

			G.f.: A(x) = 1 + 4*x + 36*x^2 + 692*x^3 + 38186*x^4 + 10012732*x^5 +...
		

Crossrefs

Cf. A156631, A133991, A155201.

Programs

PARI

{a(n)=polcoeff(sum(j=0,n,sum(k=1, n, ((2^j+2^k)*x)^k/k+x*O(x^n))^j/j!),n)}