A370281 Coefficient of x^n in the expansion of 1/( (1-x)^2 - x^3 )^n.

1, 2, 10, 59, 370, 2392, 15757, 105156, 708546, 4809695, 32841380, 225321967, 1552063981, 10726766624, 74348039020, 516586596484, 3597106344450, 25095046641861, 175369603836301, 1227366066102925, 8601637753421020, 60355768595163030, 423972992316330225

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-1,k) * binomial(3*n-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)^2 - x^3) ). See A369214.

Prog

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

Crossrefs

Cf. A369214.

Sequence in context: A372415 A372476 A262910 * A351502 A202482 A240605

Adjacent sequences: A370278 A370279 A370280 * A370282 A370283 A370284

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved