A371607 G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^2) )^2.

1, 2, 3, 10, 29, 92, 314, 1078, 3830, 13844, 50746, 188554, 707667, 2679960, 10227940, 39294772, 151859858, 589943516, 2302462140, 9023681820, 35498194465, 140122652960, 554827907272, 2203135245820, 8771143399104, 35003747271444, 140002994665366

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137954.

Prog

(PARI) a(n, r=2, s=1, t=0, 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. A137954, A371612.

Sequence in context: A084380 A363139 A286814 * A338583 A121909 A153909

Adjacent sequences: A371604 A371605 A371606 * A371608 A371609 A371610

Keyword

nonn

Author

Seiichi Manyama, Mar 29 2024

Status

approved