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 A136596 Column 2 of triangle A136595. 4
 1, -3, 31, -375, 5911, -113463, 2571031, -67170855, 1987919671, -65731585623, 2401646633431, -96089053104135, 4178215255335031, -196193483904124983, 9894077286353278231, -533334378459657706215, 30602112192036616407991 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS FORMULA 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, Jan 27 2008 PROG (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))} for(n=2, 20, print1(a(n), ", ")) (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!)} for(n=2, 20, print1(a(n), ", ")) CROSSREFS Cf. A136595; A048287, A136597. Sequence in context: A136024 A051200 A274667 * A186207 A014178 A123818 Adjacent sequences:  A136593 A136594 A136595 * A136597 A136598 A136599 KEYWORD sign AUTHOR Paul D. Hanna, Jan 10 2008 STATUS approved

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Last modified April 14 06:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)