A370270 Coefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^2)^3 )^n.

1, 2, 16, 110, 840, 6502, 51424, 411602, 3326600, 27082460, 221776016, 1824750424, 15073212648, 124926064460, 1038330110400, 8651387371360, 72238476287112, 604327981885262, 5064140053702240, 42500097815152940, 357157266768270840, 3005093769261481238

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n-2*k-1,n-2*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 * (1-x^2)^3 ). See A365879.

Prog

(PARI) a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));

Crossrefs

Cf. A365879.

Sequence in context: A301940 A359758 A370245 * A058121 A117627 A117628

Adjacent sequences: A370267 A370268 A370269 * A370271 A370272 A370273

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved