A378464 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-1,n-3*k).

1, 1, 3, 13, 63, 306, 1473, 7085, 34239, 166459, 813618, 3994200, 19678233, 97239130, 481740885, 2392004853, 11900655999, 59312062026, 296071376307, 1479998924447, 7407613846698, 37118966710076, 186195636158436, 934889598483048, 4698229684691913, 23629859054461331

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = [x^n] 1/(1 - x - x^3/(1 - x)^2)^n.

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(2*n-1, n-3*k));

Crossrefs

Cf. A370624, A378463.

Cf. A367413.

Sequence in context: A350478 A276893 A284160 * A092467 A034478 A026715

Adjacent sequences: A378461 A378462 A378463 * A378465 A378466 A378467

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2024

Status

approved