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A138734
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a(n) = n-th term of the (n+1)-th inverse binomial transform of A138737 for n>=0.
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1
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1, 0, 4, 0, 176, 0, 24192, 0, 6966528, 0, 3459768320, 0, 2642804895744, 0, 2880385956446208, 0, 4248075487709560832, 0, 8150896954121845211136, 0, 19738484719911211593891840, 0, 58891248341123034677673721856, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The n-th term of the n-th inverse binomial transform of A138737 = (n+1)^(n-1) for n>=0.
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FORMULA
| Contribution from Paul D. Hanna, Apr 20 2011: (Start)
a(n) = Sum_{k=0..n} (-1)^k*C(n,k) * (k+1)^(k-1) * (n-k+1)^(n-k-1).
E.g.f.: -LambertW(x)*LambertW(-x)/x^2.
E.g.f.: exp( Sum_{n>=1} 2*(2n)^(2n-1) * x^(2n)/(2n)! ).
(End)
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PROG
| (PARI) {a(n)=local(A=[1]); for(k=1, n, A=concat(A, 0); A[k+1]=(k+1)^(k-1)-polcoeff(subst(Ser(A), x, x/(1+k*x+x*O(x^k)))/(1+k*x), k)); polcoeff(subst(Ser(A), x, x/(1+(n+1)*x+x*O(x^n)))/(1+(n+1)*x), n)}
(PARI) {a(n)=sum(k=0, n, (-1)^k*binomial(n, k)*(k+1)^(k-1)*(n-k+1)^(n-k-1))}
(PARI) {a(n)=local(LW=sum(m=1, n+1, m^(m-1)*x^m/m!)+x^2*O(x^n)); n!*polcoeff(-LW*subst(LW, x, -x)/x^2, n)}
(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, 2*(2*m)^(2*m-1)*x^(2*m)/(2*m)!)+x*O(x^n)), n)}
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CROSSREFS
| Cf. A138737.
Sequence in context: A013037 A129814 A129825 * A119010 A176050 A099841
Adjacent sequences: A138731 A138732 A138733 * A138735 A138736 A138737
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 05 2008
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