A208677 G.f.: 1 = Sum_{n>=1} a(n) * x^n*(1-x)^(n+1) / Product_{k=1..n} (1 + (k+2)*x).

1, 1, 5, 34, 287, 2863, 32746, 420736, 5983449, 93133215, 1572620167, 28601774854, 556966811404, 11554566786712, 254272882352574, 5913584928252552, 144873520289993221, 3727881181448196395, 100497262518486193227, 2831814367381689184110, 83232066231023514044175

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+2, 2) / 3.

Example

 1 = 1*(1-x) + 1*x*(1-x)^2/((1+3*x)) + 5*x^2*(1-x)^3/((1+3*x)*(1+4*x)) + 34*x^3*(1-x)^4/((1+3*x)*(1+4*x)*(1+5*x)) + 287*x^4*(1-x)^5/((1+3*x)*(1+4*x)*(1+5*x)*(1+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+(j+2)*x+x*O(x^n))), n))}
for(n=0, 22, print1(a(n), ", "))

Crossrefs

Cf. A132623, A132624, A208676, A208678.

Sequence in context: A211794 A289147 A284864 * A259906 A355258 A334066

Adjacent sequences: A208674 A208675 A208676 * A208678 A208679 A208680

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2012

Status

approved