A379193 G.f. A(x) satisfies A(x) = (1 + x*A(x))^2/(1 - x*A(x)^2).

1, 3, 16, 113, 921, 8161, 76362, 742402, 7425651, 75918094, 789808133, 8334087494, 88983204682, 959557630166, 10435688564260, 114329775220590, 1260613164978289, 13978381013355836, 155778935125738138, 1743836357339342353, 19599785557100463390, 221094189317073465597, 2502296315746442064053

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

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

Crossrefs

Cf. A379194.

Sequence in context: A097142 A039751 A005419 * A332024 A124537 A355720

Adjacent sequences: A379190 A379191 A379192 * A379194 A379195 A379196

Keyword

nonn

Author

Seiichi Manyama, Dec 17 2024

Status

approved