A377706 G.f. A(x) satisfies A(x) = 1 + x/A(x)^3 * (1 - A(x) + A(x)^4).

1, 1, 0, 3, -6, 28, -105, 444, -1897, 8338, -37305, 169471, -779537, 3623500, -16993990, 80316081, -382136133, 1828896726, -8798796709, 42528048930, -206413678447, 1005623593109, -4916026689088, 24106987842416, -118551374861525, 584526569727010, -2888995759466360

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = (1/n) * Sum_{k=0..n} (-1)^k * binomial(n,k) * binomial(n-4*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-4*k, n-k-1))/n);

Crossrefs

Cf. A317133, A364759, A377458, A378958, A378920.

Cf. A371890.

Sequence in context: A128056 A068808 A068133 * A370668 A220823 A024497

Adjacent sequences: A377703 A377704 A377705 * A377707 A377708 A377709

Keyword

sign,new

Author

Seiichi Manyama, Dec 12 2024

Status

approved