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A100249 Antidiagonal sums of the slanted Catalan convolution table A100247. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A248652 A158027 A346776 * A138477 A182240 A052102

Adjacent sequences:  A100246 A100247 A100248 * A100250 A100251 A100252

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 09 2004

STATUS

approved

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Last modified October 28 13:18 EDT 2021. Contains 348329 sequences. (Running on oeis4.)