A370242 Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^2) )^n.

1, 2, 12, 74, 480, 3202, 21756, 149746, 1040640, 7285538, 51307212, 363057114, 2579270304, 18385404546, 131429288828, 941857237474, 6764184258560, 48671099313730, 350799656912652, 2532218940625642, 18303373070813280, 132462237913391362, 959699439413581692

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(n,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) ). See A369208.

Prog

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

Crossrefs

Cf. A288470, A370245.

Cf. A240688, A369208.

Sequence in context: A378404 A360318 A074616 * A352373 A006936 A052875

Adjacent sequences: A370239 A370240 A370241 * A370243 A370244 A370245

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved