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A130522 Diagonal immediately below the main diagonal of triangle A130521. 1
1, 1, 3, 8, 25, 89, 349, 1496, 6962, 34861, 186678, 1063591, 6418167, 40860485, 273513831, 1919284246, 14080876273, 107750778177, 858195666410, 7100543662976, 60922480229704, 541193416875432, 4970306167860426 (list; graph; refs; listen; history; text; internal format)
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 A009268 A024430

Adjacent sequences:  A130519 A130520 A130521 * A130523 A130524 A130525

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 02 2007

STATUS

approved

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Last modified September 21 15:32 EDT 2017. Contains 292312 sequences.