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Search: id:A138736
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| 1, 1, 4, 36, 368, 5200, 90432, 1884736, 45817088, 1273874688, 39891461120, 1389816423424, 53334303584256, 2235679577657344, 101651458028158976, 4983219643056537600, 262026143585449607168, 14711289584591513387008
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OFFSET
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0,3
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COMMENT
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The n-th term of the n-th inverse binomial transform of A138737 equals (n+1)^(n-1) for n>=0.
Related to LambertW(-x)/(-x) = Sum_{n>=0} (n+1)^(n-1)*x^n/n!.
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FORMULA
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O.g.f. satisfies: [x^n] A( x/(1+(n-1)*x) )/(1+(n-1)*x) = (n+1)^(n-1) for n>=0.
E.g.f. satisfies: [x^n] A(x)*exp(-(n-1)*x) = (n+1)^(n-1)/n! for n>=0.
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PROGRAM
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(PARI) {a(n)=local(A=[1]); for(k=1, n, A=concat(A, 0); A[k+1]=(k+1)^(k-1)-Vec(subst(Ser(A), x, x/(1+(k-1)*x+x*O(x^k)))/(1+(k-1)*x))[k+1]); A[n+1]}
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CROSSREFS
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Cf. A138737.
Sequence in context: A000765 A026334 A163455 this_sequence A019999 A002894 A131765
Adjacent sequences: A138733 A138734 A138735 this_sequence A138737 A138738 A138739
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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), Apr 05 2008
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