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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
1, 4, 36, 692, 38186, 10012732, 14013453284, 89892733239928, 2455110210935634790, 278266942487534934333100, 129264916198375365693754194988, 244287539590735476133066282560012360 (list; graph; refs; listen; history; text; internal format)
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: A208732 A029989 A163887 * A289545 A322782 A145565

Adjacent sequences:  A156627 A156628 A156629 * A156631 A156632 A156633

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 12 2009

STATUS

approved

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Last modified May 22 05:51 EDT 2022. Contains 353933 sequences. (Running on oeis4.)