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A377148
a(n) = Sum_{k=0..n} binomial(k+3,3) * binomial(k,n-k)^2.
7
1, 4, 14, 60, 225, 796, 2764, 9304, 30580, 98700, 313422, 981548, 3037473, 9301620, 28222000, 84927760, 253699285, 752863840, 2220831160, 6515581600, 19021079866, 55276625304, 159967084164, 461150383400, 1324652146775, 3792447499916, 10824189204014
OFFSET
0,2
FORMULA
G.f.: (1-x-x^2) * ((1-x-x^2)^2 + 6*x^3) / ((1-x-x^2)^2 - 4*x^3)^(7/2).
PROG
(PARI) a(n) = sum(k=0, n, binomial(k+3, 3)*binomial(k, n-k)^2);
(PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=3, M=30, x='x+O('x^M), X=1-x-x^2, Y=3); Vec(sum(k=0, N\2, a089627(N, k)*X^(N-2*k)*x^(Y*k))/(X^2-4*x^Y)^(N+1/2))
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 18 2024
STATUS
approved