A366453 G.f. A(x) satisfies A(x) = 1 + x + x*A(x)^(7/2).

1, 2, 7, 42, 287, 2142, 16898, 138600, 1170037, 10098774, 88712736, 790540296, 7128879940, 64933227996, 596523624144, 5520761026854, 51424824505054, 481741853731110, 4535711525840271, 42897532229559714, 407358615638833341, 3882484733036731500

Offset

0,2

Links

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

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366405.

a(n) = Sum_{k=0..n} binomial(5*k/2+1,n-k) * binomial(7*k/2,k) / (5*k/2+1).

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A295537. - Seiichi Manyama, Apr 04 2024

Prog

(PARI) a(n) = sum(k=0, n, binomial(5*k/2+1, n-k)*binomial(7*k/2, k)/(5*k/2+1));

Crossrefs

Cf. A112478, A364393, A364407, A364408, A364409, A366266, A366267, A366268, A366452, A366454, A366455, A366456.

Cf. A295537, A366405.

Sequence in context: A265772 A109172 A131682 * A345368 A353257 A368449

Adjacent sequences: A366450 A366451 A366452 * A366454 A366455 A366456

Keyword

nonn

Author

Seiichi Manyama, Oct 10 2023

Status

approved