A370212 Coefficient of x^n in the expansion of ( (1+x) / (1-x^3) )^n.

1, 1, 1, 4, 17, 51, 142, 442, 1457, 4702, 14951, 48038, 156158, 508860, 1658112, 5414754, 17735473, 58209803, 191310964, 629605300, 2074916167, 6846553375, 22615507300, 74775856026, 247463508542, 819645776926, 2716912851446, 9012261102106, 29914317146864

Offset

0,4

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(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) * (1-x^3) ). See A215340.

Prog

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

Crossrefs

Cf. A215340.

Sequence in context: A184445 A334694 A228960 * A131339 A362173 A047668

Adjacent sequences: A370209 A370210 A370211 * A370213 A370214 A370215

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2024

Status

approved