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A370184
Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^3) )^n.
1
1, 3, 15, 87, 539, 3458, 22659, 150594, 1011131, 6841779, 46577430, 318654900, 2188931699, 15087882943, 104301302218, 722840860787, 5020500381131, 34937184351049, 243539967641271, 1700255814753027, 11886457488148674, 83200718154710607, 583026777685802256
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(3*n-k,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 * (1+x+x^3)) ). See A369482.
PROG
(PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 11 2024
STATUS
approved