A370284 Coefficient of x^n in the expansion of 1/( (1-x)^3 - x^3 )^n.

1, 3, 21, 168, 1425, 12483, 111594, 1011636, 9264753, 85510590, 794087151, 7410887718, 69446624910, 653019755430, 6158495001960, 58226492157048, 551725482707505, 5238008159399163, 49814314319342424, 474467729545936650, 4525387365179378775

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(4*n-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 - x^3) ). See A369114.

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(4*n-1, n-3*k));

Crossrefs

Cf. A369114.

Sequence in context: A361375 A371771 A214391 * A046637 A220103 A132805

Adjacent sequences: A370281 A370282 A370283 * A370285 A370286 A370287

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved