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A156630
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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.
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1
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1, 4, 36, 692, 38186, 10012732, 14013453284, 89892733239928, 2455110210935634790, 278266942487534934333100, 129264916198375365693754194988, 244287539590735476133066282560012360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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EXAMPLE
| G.f.: A(x) = 1 + 4*x + 36*x^2 + 692*x^3 + 38186*x^4 + 10012732*x^5 +...
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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)}
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CROSSREFS
| Cf. A156631, A133991, A155201.
Sequence in context: A135867 A029989 A163887 * A145565 A126152 A009446
Adjacent sequences: A156627 A156628 A156629 * A156631 A156632 A156633
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 12 2009
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