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A088716
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G.f. satisfies: A(x) = 1 + x*A(x)*d/dx[x*A(x)] = 1 + x*A(x)^2 + x^2*A(x)*A'(x).
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11
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1, 1, 3, 14, 85, 621, 5236, 49680, 521721, 5994155, 74701055, 1003125282, 14437634276, 221727608284, 3619710743580, 62605324014816, 1143782167355649, 22014467470369143, 445296254367273457, 9444925598142843970
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(0)=1, a(n) = sum(k=1, n, k*a(k-1)*a(n-k) ). G.f.: A(x) = serreverse(x/f(x))/x where f(x) is the g.f. of A088715.
Self-convolution is A112916, where a(n) = (n+1)/2*A112916(n-1) for n>0.
O.g.f.: A(x) = log(G(x))/x where G(x) is the e.g.f. of A182962 given by:
. G(x) = exp( x/(1 - x*G'(x)/G(x)) ). [From Paul D. Hanna, Jan 01 2011]
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PROG
| (PARI) a(n)=if(n==0, 1, sum(k=0, n-1, (k+1)*a(k)*a(n-k-1)))
(PARI) {a(n)=local(G=1+x); for(i=1, n, G=exp(x/(1 - x*deriv(G)/G+x*O(x^n)))); polcoeff(log(G)/x, n)} [From Paul D. Hanna, Jan 01 2011]
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CROSSREFS
| Cf. A112916 (A^2), A112911, A112912, A112913, A112914, A088715, A182962.
Sequence in context: A088717 A111538 A160881 * A005189 A074520 A127715
Adjacent sequences: A088713 A088714 A088715 * A088717 A088718 A088719
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 12 2003
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