OFFSET
3,2
FORMULA
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).
PROG
(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!)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jan 10 2008
STATUS
approved