A136597 Column 3 of triangle A136595.

1, -6, 85, -1350, 26341, -603246, 15887845, -473148150, 15723174181, -576826897086, 23157022930405, -1009818279438150, 47533643556874021, -2402218856253008526, 129730266330534913765, -7455932648513351731350, 454377365410347843373861

Offset

3,2

Links

Table of n, a(n) for n=3..19.

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

Cf. A136595, A048287, A136596.

Sequence in context: A167252 A290011 A164266 * A064329 A187740 A332407

Adjacent sequences: A136594 A136595 A136596 * A136598 A136599 A136600

Keyword

sign

Author

Paul D. Hanna, Jan 10 2008

Status

approved