A370213 Coefficient of x^n in the expansion of ( (1+x)^2 / (1-x^3) )^n.

1, 2, 6, 23, 102, 477, 2265, 10831, 52134, 252581, 1230831, 6027012, 29630793, 146162525, 723042585, 3585576123, 17819138214, 88723077165, 442503268107, 2210287317913, 11055220684527, 55362552116104, 277553123875572, 1392884816721228, 6996589905913737

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

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

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3) ). See A369398.

Prog

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

Crossrefs

Cf. A369398.

Sequence in context: A279572 A263576 A370196 * A231444 A248900 A376395

Adjacent sequences: A370210 A370211 A370212 * A370214 A370215 A370216

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2024

Status

approved