A378954 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^3/(1 + x*A(x)^2) )^2.

1, 2, 11, 82, 705, 6584, 64902, 664608, 7001006, 75378082, 825810304, 9176278104, 103171720299, 1171558985630, 13416903518301, 154784357304138, 1797153050309355, 20984321920535966, 246252819129444579, 2902768234099178002, 34355158795966317996, 408086199665333171952

Offset

0,2

Links

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

Formula

G.f. A(x) satisfies:

(1) A(x) = 1/( 1 - x*A(x)^(5/2)/(1 + x*A(x)^2) )^2.

(2) A(x) = 1 + x * A(x)^2 * (1 + A(x)^(3/2)).

(3) A(x) = B(x)^2 where B(x) is the g.f. of A364765.

If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(s*k,n-k)/(t*k+u*(n-k)+r).

Prog

(PARI) a(n, r=2, s=-1, t=6, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A364765, A378952.

Cf. A262441, A366400, A370474.

Sequence in context: A215654 A330677 A209094 * A293574 A322644 A243408

Adjacent sequences: A378951 A378952 A378953 * A378957 A378958 A378964

Keyword

nonn,new

Author

Seiichi Manyama, Dec 12 2024

Status

approved