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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
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.
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 12 2009
STATUS
approved