A365690 G.f. satisfies A(x) = 1 + x^2*A(x)^4 / (1 - x*A(x)).

1, 0, 1, 1, 5, 10, 38, 101, 353, 1070, 3659, 11843, 40505, 135873, 468104, 1604375, 5576315, 19386656, 67950717, 238676813, 842797959, 2983745508, 10603445402, 37777263153, 134985354179, 483438728094, 1735527037388, 6243193190117, 22503637842423

Offset

0,5

Links

Table of n, a(n) for n=0..28.

Formula

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

Prog

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

Crossrefs

Cf. A004148, A005043, A025246, A046736, A365691.

Cf. A365692.

Sequence in context: A270219 A270276 A271604 * A277816 A359021 A355327

Adjacent sequences: A365687 A365688 A365689 * A365691 A365692 A365693

Keyword

nonn

Author

Seiichi Manyama, Sep 16 2023

Status

approved