A366097 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^4 ).

1, 3, 12, 56, 287, 1564, 8896, 52217, 313955, 1923775, 11970066, 75427608, 480365740, 3086989128, 19992893796, 130363352003, 855099212950, 5638480905533, 37354602517624, 248515024509486, 1659620048332369, 11121368629141886, 74759777174598964

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A366071, A366095, A366096.

Sequence in context: A192132 A179486 A369482 * A074533 A000257 A301418

Adjacent sequences: A366094 A366095 A366096 * A366098 A366099 A366100

Keyword

nonn

Author

Seiichi Manyama, Sep 29 2023

Status

approved