A243922 G.f.: 1 = Sum_{n>=0} a(n) * x^n*(1-x)^(n+1) / Product_{k=1..n} (1 + 2*(k+2)*x).

1, 1, 8, 87, 1186, 19328, 365120, 7824589, 187217370, 4940474068, 142398668848, 4447556785374, 149541503654196, 5382913372109528, 206455211385309248, 8402342525589672769, 361557591510622222090, 16397474363912261372852, 781575694749373121466960, 39053517651541054156854082

Offset

0,3

Comments

Triangle T = A243920 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) = 2*n+1 and T(n,n)=0 for n>=0.

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = A243920(n+2,2) / 5.

Example

G.f.: 1 = 1*(1-x) + 1*x*(1-x)^2/(1+2*3*x) + 8*x^2*(1-x)^3/((1+2*3*x)*(1+2*4*x)) + 87*x^3*(1-x)^4/((1+2*3*x)*(1+2*4*x)*(1+2*5*x)) + 1186*x^4*(1-x)^5/((1+2*3*x)*(1+2*4*x)*(1+2*5*x)*(1+2*6*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+2*(j+2)*x+x*O(x^n))), n))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A243920, A243921, A243923, A208677.

Sequence in context: A307822 A225613 A358982 * A239753 A246512 A366233

Adjacent sequences: A243919 A243920 A243921 * A243923 A243924 A243925

Keyword

nonn

Author

Paul D. Hanna, Jun 15 2014

Status

approved