A379249 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x*A(x))^2.

1, 3, 18, 148, 1403, 14417, 156161, 1755664, 20293341, 239654554, 2879027132, 35072400492, 432238230583, 5379422216020, 67513288465855, 853481985400772, 10858099927189575, 138912471444569435, 1786014309638224994, 23065160118446902506, 299062458173041384523

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..873

Robert Israel, Linear recurrence of order 20

Formula

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

D-finite with a recurrence of order 20 (see link). - Robert Israel, May 06 2026

Prog

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

Crossrefs

Cf. A198953, A379190.

Sequence in context: A371825 A240921 A373771 * A221961 A385500 A138420

Adjacent sequences: A379246 A379247 A379248 * A379250 A379251 A379252

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2024

Status

approved