A370248 Coefficient of x^n in the expansion of ( 1/(1-x) * (1+x^3)^2 )^n.

1, 1, 3, 16, 67, 276, 1200, 5293, 23427, 104425, 468428, 2110725, 9546256, 43315546, 197088195, 898910916, 4108495491, 18812770011, 86285313327, 396332663094, 1822878714492, 8394131895424, 38696042930251, 178561943852670, 824720550229584, 3812313399877776

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(2*n-3*k-1,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) / (1+x^3)^2 ). See A369266.

Prog

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

Crossrefs

Cf. A369266, A370214.

Sequence in context: A248016 A000269 A378406 * A370274 A015524 A012279

Adjacent sequences: A370245 A370246 A370247 * A370249 A370250 A370251

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved