A379171 G.f. A(x) satisfies A(x) = (1 + x)/(1 - x*A(x))^3.

1, 4, 21, 139, 1021, 8010, 65708, 556751, 4834686, 42800265, 384832083, 3504693519, 32261240127, 299685628629, 2805773759322, 26448278629697, 250806022116194, 2390973659474304, 22901157688878983, 220279614235505630, 2126890041331033797, 20606993367985131716

Offset

0,2

Links

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

Formula

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

Prog

(PARI) a(n) = sum(k=0, n, binomial(n-k+1, k)*binomial(4*n-4*k+2, n-k)/(n-k+1));

Crossrefs

Cf. A365764, A369215, A379172.

Cf. A025227, A379173.

Sequence in context: A180399 A349534 A222058 * A380228 A265174 A087761

Adjacent sequences: A379167 A379169 A379170 * A379172 A379173 A379174

Keyword

nonn

Author

Seiichi Manyama, Dec 17 2024

Status

approved