A366096 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^3 ).

1, 2, 5, 15, 51, 187, 719, 2858, 11650, 48438, 204630, 875867, 3790172, 16554305, 72883035, 323109570, 1441152303, 6462494515, 29118219850, 131761291852, 598529262016, 2728346941040, 12476533435028, 57220220120080, 263125059775970, 1212942573227309

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(2*n-k+2,n-3*k).

Prog

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

Crossrefs

Cf. A366071, A366095, A366097.

Sequence in context: A367414 A073525 A369481 * A007317 A181768 A279554

Adjacent sequences: A366093 A366094 A366095 * A366097 A366098 A366099

Keyword

nonn

Author

Seiichi Manyama, Sep 29 2023

Status

approved