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Search: id:A120016
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| A120016 |
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a(n) = A120014(n)/n = coefficient of x^n, divided by n, in the n-th self-composition of the g.f. of A120009 for n>=1. |
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+0
3
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| 1, 1, 3, 15, 106, 982, 11383, 159595, 2636590, 50278058, 1088631886, 26409797526, 710034913212, 20963748887980, 674521750652735, 23497037813799795, 881180319357526102, 35400836754598975554, 1516991897621421273210
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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a(n) = [x^n] (x/n)*((1-n+n^2) - n^2*(n+1)*x - n*(1-(n+2)*x)*C(x) )/(1-n+n^2*x)^2, where C(x) = (1-sqrt(1-4*x))/(2*x) is the Catalan function (A000108).
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PROGRAM
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(PARI) {a(n)=local(k=n, x=X+X^3*O(X^n)); (1/n)*polcoeff( x*((1-k+k^2)-k^2*(k+1)*x-k*(1-(k+2)*x)*(1-sqrt(1-4*x))/2/x)/(1-k+k^2*x)^2, n, X)}
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CROSSREFS
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Cf. A120009, A120014, A120022; A000108.
Sequence in context: A088109 A128276 A107878 this_sequence A074519 A105618 A120732
Adjacent sequences: A120013 A120014 A120015 this_sequence A120017 A120018 A120019
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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), Jun 07 2006
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