A208676 G.f.: 1 = Sum_{n>=1} a(n) * x^n*(1-x)^(n+1) / Product_{k=1..n} (1 + (k+1)*x).

1, 1, 4, 23, 169, 1496, 15400, 180055, 2350867, 33840345, 531707256, 9045486916, 165507986668, 3238945135696, 67470601883224, 1489923969768999, 34753006977085479, 853544188578784147, 22011310309759024484, 594514290559650994575, 16780116115165946427561

Offset

0,3

Comments

Related triangle T=A132623 is generated by sums of matrix powers of itself such that:

T(n,k) = Sum_{j=1..n-k-1} [T^j](n-1,k) with T(n+1,n) = n+1 and T(n,n)=0 for n>=0.

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = A132623(n+1, 1) / 2.

Example

 1 = 1*(1-x) + 1*x*(1-x)^2/(1+2*x) + 4*x^2*(1-x)^3/((1+2*x)*(1+3*x)) + 23*x^3*(1-x)^4/((1+2*x)*(1+3*x)*(1+4*x)) + 169*x^4*(1-x)^5/((1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)) +...

Prog

 (PARI) {a(n)=if(n<0, 0, polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x)^(k+1)/prod(j=1, k, 1+(j+1)*x+x*O(x^n))), n))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A132623, A132624, A208677, A208678.

Sequence in context: A317057 A053525 A277382 * A317276 A113869 A084357

Adjacent sequences: A208673 A208674 A208675 * A208677 A208678 A208679

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2012

Status

approved