A372415 Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x)^3 )^n.

1, 2, 10, 59, 366, 2332, 15121, 99276, 657894, 4391438, 29482320, 198865680, 1346655921, 9149295482, 62336961732, 425760311734, 2914151872614, 19983724103726, 137267022656710, 944287970305935, 6504676822047876, 44861522295224400, 309742638630690264

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(3*n-2*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)^3 / (1-x+x^3) ). See A366052.

Prog

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

Crossrefs

Cf. A372413, A372414.

Cf. A366052.

Sequence in context: A309955 A340987 A186758 * A372476 A262910 A370281

Adjacent sequences: A372412 A372413 A372414 * A372416 A372417 A372418

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved