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Search: id:A136597
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| 1, -6, 85, -1350, 26341, -603246, 15887845, -473148150, 15723174181, -576826897086, 23157022930405, -1009818279438150, 47533643556874021, -2402218856253008526, 129730266330534913765, -7455932648513351731350, 454377365410347843373861
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OFFSET
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3,2
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FORMULA
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a(n) = Sum_{i=0..n-1} (-1)^i*(3+i)!*Stirling2(n,3+i)*Catalan(3,i)/3!, where Stirling2(n,k) = A008277(n,k), Catalan(k,i) = C(2*i+k,i)*k/(2*i+k) = coefficient of x^i in C(x)^k with C(x) = (1-sqrt(1-4x))/(2x).
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PROGRAM
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(PARI) {a(n)=n!/2!* sum(i=0, n-1, (-1)^i*polcoeff(((exp(x+x*O(x^n))-1)^(3+i)), n)*binomial(2*i+3, i)/(2*i+3))} (PARI) /* Define Stirling2: */ {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)} /* Define Catalan(m, n) = [x^n] C(x)^m: */ {Catalan(m, n)=binomial(2*n+m, n)*m/(2*n+m)} /* Define this sequence: */ {a(n)=sum(i=0, n-1, (-1)^i*(3+i)!*Stirling2(n, 3+i)*Catalan(3, i)/3!)}
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CROSSREFS
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Cf. A136595; A048287, A136596.
Adjacent sequences: A136594 A136595 A136596 this_sequence A136598 A136599 A136600
Sequence in context: A123312 A010794 A030031 this_sequence A064329 A091881 A004701
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 10 2008
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