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

0,2

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.

Links

Table of n, a(n) for n=0..11.

Example

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

Prog

(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)}

Crossrefs

Cf. A156631, A133991, A155201.

Sequence in context: A356616 A029989 A163887 * A289545 A322782 A145565

Adjacent sequences: A156627 A156628 A156629 * A156631 A156632 A156633

Keyword

nonn

Author

Paul D. Hanna, Feb 12 2009

Status

approved