A071969 a(n) = Sum_{k=0..floor(n/3)} (binomial(n+1, k)*binomial(2*n-3*k, n-3*k)/(n+1)).

1, 1, 2, 6, 19, 63, 219, 787, 2897, 10869, 41414, 159822, 623391, 2453727, 9733866, 38877318, 156206233, 630947421, 2560537092, 10435207116, 42689715279, 175243923783, 721649457417, 2980276087005, 12340456995177, 51222441676513, 213090270498764, 888321276659112

Offset

0,3

Comments

Diagonal of A071946. - Emeric Deutsch, Dec 15 2004

Last (largest) number of each row of A071946. - David Scambler, May 15 2012

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

D. Merlini et al., Underdiagonal lattice paths with unrestricted steps, Discrete Appl. Math., 91 (1999), 197-213 (d_n page 209).

Formula

G.f. (offset 1) is series reversion of (x-x^2)/(1+x^3).

Maple

A071969 := n->add( binomial(n+1, k)*binomial(2*n-3*k, n-3*k)/(n+1), k=0..floor(n/3));
Order:=30: g:=solve(series((H-H^2)/(1+H^3), H)=z, H): seq(coeff(g, z^n), n=1..28); # Emeric Deutsch, Dec 15 2004

Mathematica

Table[Sum[Binomial[n+1, k] Binomial[2n-3k, n-3k]/(n+1), {k, 0, Floor[n/3]}], {n, 0, 40}] (* Harvey P. Dale, Jul 20 2022 *)

Prog

(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-x^2)/(1+x^3)+x^2*O(x^n)), n+1))

Crossrefs

Cf. A071946 is the triangle and A119254 has the row sums.

Cf. A006318, A052709, A365268, A366025.

Sequence in context: A001168 A193111 A119255 * A063030 A206463 A148467

Adjacent sequences: A071966 A071967 A071968 * A071970 A071971 A071972

Keyword

nonn

Author

N. J. A. Sloane, Jun 17 2002

Status

approved