A243921 G.f.: 1 = Sum_{n>=0} a(n) * x^n*(1-x)^(n+1) / Product_{k=1..n} (1 + 2*(k+1)*x).

1, 1, 6, 53, 612, 8676, 145268, 2798355, 60852004, 1472460760, 39202586348, 1138006266618, 35750917265544, 1207874695612336, 43655110115967528, 1680097198812367783, 68578132320350944324, 2958457556868808457800, 134469635178557071054492, 6421829932908536633173110

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+1,1) / 3.

Example

G.f.: 1 = 1*(1-x) + 1*x*(1-x)^2/(1+2*2*x) + 6*x^2*(1-x)^3/((1+2*2*x)*(1+2*3*x)) + 53*x^3*(1-x)^4/((1+2*2*x)*(1+2*3*x)*(1+2*4*x)) + 612*x^4*(1-x)^5/((1+2*2*x)*(1+2*3*x)*(1+2*4*x)*(1+2*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+2*(j+1)*x+x*O(x^n))), n))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A243920, A243922, A243923, A208676.

Sequence in context: A066357 A276365 A185148 * A109092 A068416 A360231

Adjacent sequences: A243918 A243919 A243920 * A243922 A243923 A243924

Keyword

nonn

Author

Paul D. Hanna, Jun 15 2014

Status

approved