A366117 Expansion of (1/x) * Series_Reversion( x*(1+x+x^3)/(1+x)^3 ).

1, 2, 5, 13, 33, 77, 147, 128, -726, -5870, -28918, -117501, -419748, -1330265, -3631065, -7585458, -5021553, 62555365, 485450778, 2473377984, 10459876208, 38765746168, 126610935508, 352046019398, 725506704096, 264040020875, -7980075940060, -58806846330257

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

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

Prog

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

Crossrefs

Cf. A366116, A366118, A366119.

Cf. A366096.

Sequence in context: A108890 A220739 A337282 * A027929 A001659 A088921

Adjacent sequences: A366114 A366115 A366116 * A366118 A366119 A366120

Keyword

sign

Author

Seiichi Manyama, Sep 29 2023

Status

approved