A381876 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^3, where C(x) is the g.f. of A000108.

1, 4, 23, 156, 1167, 9311, 77710, 670294, 5928183, 53467931, 489904745, 4547296624, 42667426369, 404044679434, 3856480309376, 37062228265769, 358330619946164, 3482936427997599, 34014454418349579, 333598711996924548, 3284326412065118717, 32446900771699499147

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(4*n-4*k+2,n-k)/(n+k+1).

a(n) = binomial(2 + 4*n, n)*hypergeom([-2/3-n, -1/3-n, -n, 1+n], [-1/2-n, -1/4-n, 1/4-n], 3^3/2^8)/(1 + n). - Stefano Spezia, Mar 09 2025

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+2, n-k)/(n+k+1));

Crossrefs

Cf. A129442, A381875, A381877.

Cf. A000108, A381880.

Sequence in context: A374564 A007297 A263843 * A326350 A198916 A182969

Adjacent sequences: A381873 A381874 A381875 * A381877 A381878 A381879

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2025

Status

approved