A378730 G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)^(3/2)) )^2.

1, 2, 3, 10, 35, 134, 544, 2288, 9907, 43830, 197300, 900738, 4160521, 19408084, 91302317, 432663728, 2063421045, 9896113574, 47698770359, 230932635206, 1122545149941, 5476405604806, 26805046064328, 131595640014314, 647829955225386, 3197267300375652

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: A(x) = (1 + x*B(x))^2 where B(x) is the g.f. of A364742.

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(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

Prog

(PARI) a(n, r=2, s=1, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A364742, A365119.

Sequence in context: A059735 A358213 A356926 * A134959 A270367 A056607

Adjacent sequences: A378722 A378723 A378729 * A378731 A378732 A378733

Keyword

nonn,new

Author

Seiichi Manyama, Dec 05 2024

Status

approved