A370280 Coefficient of x^n in the expansion of 1/( (1-x)^2 - x )^n.

1, 3, 25, 234, 2305, 23373, 241486, 2527920, 26720529, 284555700, 3048323135, 32812937820, 354619072990, 3845377105794, 41817926091120, 455893204069944, 4980851709418353, 54521955043418925, 597823622561048020, 6564929893462467450, 72189820135528858455

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

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

Crossrefs

Cf. A069723, A370282.

Cf. A249924.

Sequence in context: A118726 A372458 A066221 * A367786 A332468 A134272

Adjacent sequences: A370277 A370278 A370279 * A370281 A370282 A370283

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved