A371615 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^2 )^2.

1, 2, 5, 34, 222, 1622, 12559, 100904, 835322, 7070574, 60922335, 532566850, 4711614912, 42106192680, 379544358032, 3446755447528, 31504896429042, 289619348156494, 2675953520657839, 24836797229730316, 231461661673958896, 2165002179076830442

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(n+k-1,n-k)/(3*(n-k)+1).

Prog

(PARI) a(n, r=2, s=2, t=0, u=6) = 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. A371613, A371617.

Sequence in context: A298945 A027303 A357446 * A356772 A307143 A052695

Adjacent sequences: A371612 A371613 A371614 * A371616 A371617 A371618

Keyword

nonn

Author

Seiichi Manyama, Mar 29 2024

Status

approved