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Search: id:A112915
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| A112915 |
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Recurrence: a(n) = Sum_{k=0..n-1} (k+1)*(n-k)*a(k)*a(n-k-1) for n>0, with a(0)=1. |
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+0
2
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| 1, 1, 4, 28, 272, 3312, 47872, 794880, 14840064, 306900736, 6953989120, 171200048128, 4548965384192, 129742326218752, 3953689388187648, 128215703582343168, 4409347536459988992, 160304460015345795072
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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A(x) = 1 + x*G(2*x)^2, where G(x) = g.f. of A088716, such that a(n) = 2^n*A088716(n)/(n+1) for n>=0. Also, a(n) = 2^(n-1)*A112916(n-1) for n>0.
G.f. satisfies: A(x) = 1 + x*(d/dx[x*A(x)])^2 = 1 + x*(A(x) + x*A'(x))^2.
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PROGRAM
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(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, (k+1)*(n-k)*a(k)*a(n-k-1)))
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x*deriv(x*F)^2); return(polcoeff(F, n, x))}
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CROSSREFS
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Cf. A088716, A112916.
Sequence in context: A064340 A002895 A138272 this_sequence A129683 A081917 A128318
Adjacent sequences: A112912 A112913 A112914 this_sequence A112916 A112917 A112918
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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), Oct 06 2005
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