A130522 Diagonal immediately below the main diagonal of triangle A130521.

1, 1, 3, 8, 25, 89, 349, 1496, 6962, 34861, 186678, 1063591, 6418167, 40860485, 273513831, 1919284246, 14080876273, 107750778177, 858195666410, 7100543662976, 60922480229704, 541193416875432, 4970306167860426

Offset

0,3

Comments

G.f. of column 0 (A127782) satisfies: G(x) = 1 + x*G(x+x^2); main diagonal of triangle A130521 equals column 0 shift left one place.

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..[n/2]+1} [C(n-k,k) + C(n-k+1,k-1)]*a(n-k-1) for n>=2, with a(0)=a(1)=1.

Prog

(PARI) {a(n)=if(n<0, 0, if(n<=1, 1, sum(k=0, n\2+1, (binomial(n-k, k)+binomial(n-k+1, k-1))*a(n-k-1))))}

Crossrefs

Cf. A130521 (triangle), A127782 (column 0).

Sequence in context: A190343 A185043 A033483 * A006219 A353406 A009268

Adjacent sequences: A130519 A130520 A130521 * A130523 A130524 A130525

Keyword

nonn

Author

Paul D. Hanna, Jun 02 2007

Status

approved