A378957 G.f. A(x) satisfies A(x) = ( (1 + x * A(x)^9) / (1 - x) )^(1/2).

1, 1, 5, 41, 399, 4263, 48335, 571061, 6953854, 86659366, 1099882862, 14168133882, 184756656826, 2434227814578, 32354612273352, 433312539103431, 5841624625609747, 79211315586085551, 1079630126313403483, 14782787622359779197, 203248589087860373309, 2804882047701189052925

Offset

0,3

Links

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

Formula

G.f. A(x) satisfies:

(1) A(x) = 1 + x * A(x)^2 * (1 - A(x) + A(x)^2 - A(x)^3 + A(x)^4 - A(x)^5 + A(x)^6).

(2) A(x) = sqrt(B(x)) where B(x) is the g.f. of A366402.

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

Prog

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

Crossrefs

Cf. A000108, A219537, A370473.

Cf. A366402.

Sequence in context: A156153 A026000 A058475 * A199684 A177506 A064087

Adjacent sequences: A378952 A378953 A378954 * A378958 A378964 A378967

Keyword

nonn,new

Author

Seiichi Manyama, Dec 12 2024

Status

approved