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Search: id:A136596
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| 1, -3, 31, -375, 5911, -113463, 2571031, -67170855, 1987919671, -65731585623, 2401646633431, -96089053104135, 4178215255335031, -196193483904124983, 9894077286353278231, -533334378459657706215, 30602112192036616407991
(list; graph; listen)
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OFFSET
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2,2
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FORMULA
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a(n) = Sum_{i=0..n-1} (-1)^i*(2+i)!*Stirling2(n,2+i)*Catalan(2,i)/2!, where Stirling2(n,k) = A008277(n,k); Catalan(k,i) = binomial(2*i+k,i)*k/(2*i+k) = coefficient of x^i in C(x)^k with C(x) = (1-sqrt(1-4x))/(2x).
a(n) = (1+(-1)^n*A048287(n))/2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 27 2008
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PROGRAM
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(PARI) {a(n)=n!* sum(i=0, n-1, (-1)^i*polcoeff(((exp(x+x*O(x^n))-1)^(2+i)), n)*binomial(2*i+2, i)/(2*i+2))} (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*(2+i)!*Stirling2(n, 2+i)*Catalan(2, i)/2!)}
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CROSSREFS
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Cf. A136595; A048287, A136597.
Adjacent sequences: A136593 A136594 A136595 this_sequence A136597 A136598 A136599
Sequence in context: A152276 A136024 A051200 this_sequence A014178 A123818 A087591
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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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