A366051 Expansion of (1/x) * Series_Reversion( x/(1-x+x^3) ).

1, -1, 1, 0, -3, 9, -16, 13, 29, -157, 391, -562, -32, 3002, -10373, 20747, -18083, -47941, 271117, -712216, 1066699, 122131, -6464446, 22907125, -46951992, 40883304, 120187926, -679375906, 1809757015, -2731745887, -468147579, 17768126376, -63256877763

Offset

0,5

Links

Table of n, a(n) for n=0..32.

Formula

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

Prog

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

Crossrefs

Cf. A049128, A114997, A366052, A366053.

Cf. A071879.

Sequence in context: A174179 A076362 A336970 * A070066 A299636 A271491

Adjacent sequences: A366048 A366049 A366050 * A366052 A366053 A366054

Keyword

sign

Author

Seiichi Manyama, Sep 27 2023

Status

approved