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Search: id:A159596
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| A159596 |
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G.f.: A(x) = exp( Sum_{n>=1} [ D^n x/(1-x)^2 ]^n/n ), where differential operator D = x*d/dx. |
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+0
4
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| 1, 1, 5, 22, 121, 863, 8476, 118131, 2361313, 67467236, 2731757961, 156417295405, 12605225573076, 1432381581679361, 229016092616239411, 51628631138952017332, 16402709158903948390585, 7351149638643155728435357
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^(n+1)*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.
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EXAMPLE
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G.f.: A(x) = 1 + x + 5*x^2 + 22*x^3 + 121*x^4 + 863*x^5 +...
log(A(x)) = Sum_{n>=1} [x + 2^(n+1)*x^2 + 3^(n+1)*x^3 +...]^n/n.
D^n x/(1-x)^2 = x + 2^(n+1)*x^2 + 3^(n+1)*x^3 + 4^(n+1)*x^4 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=1, n, k^(m+1)*x^k+x*O(x^n))^m/m))); polcoeff(A, n)}
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CROSSREFS
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Cf. A156170, A159597, A159598.
Sequence in context: A131460 A062794 A036235 this_sequence A020077 A033462 A111154
Adjacent sequences: A159593 A159594 A159595 this_sequence A159597 A159598 A159599
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 05 2009
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