A377705 G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 - A(x) + A(x)^3).

1, 1, 0, 2, -3, 12, -35, 121, -413, 1464, -5265, 19249, -71236, 266443, -1005511, 3824055, -14641264, 56389272, -218315173, 849170605, -3316817080, 13004273475, -51160638706, 201901154910, -799059730844, 3170706566751, -12611882813645, 50277271079611

Offset

0,4

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A115344, A127897, A364758, A365225, A378892.

Cf. A371889.

Sequence in context: A072440 A135522 A353831 * A107240 A099171 A268561

Adjacent sequences: A377702 A377703 A377704 * A377706 A377707 A377708

Keyword

sign,new

Author

Seiichi Manyama, Dec 12 2024

Status

approved