A100249 Antidiagonal sums of the slanted Catalan convolution table A100247.

1, 1, 2, 3, 6, 15, 29, 63, 160, 333, 749, 1914, 4135, 9490, 24335, 53791, 125104, 321521, 721887, 1694914, 4362855, 9907851, 23429158, 60379623, 138320021, 328917615, 848432824, 1957091277, 4674847097, 12067450014, 27992976565

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = Sum_{k=0..[2n/3]} C(n+k-[k/2], k)*(n-k-[k/2])/(n+k-[k/2]), with a(0)=1. G.f. A(x) satisfies: A(x^2) = ((1+x)/(2*x-(1-sqrt(1-4*x^3)))-(1-x)/(2*x+(1-sqrt(1+4*x^3)))).

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=0, (2*n)\3, binomial(n+k-(k\2), k)*(n-k-(k\2))/(n+k-(k\2))))}

Crossrefs

Cf. A100247.

Sequence in context: A158027 A346776 A371570 * A138477 A375278 A182240

Adjacent sequences: A100246 A100247 A100248 * A100250 A100251 A100252

Keyword

nonn

Author

Paul D. Hanna, Nov 09 2004

Status

approved