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A377153
a(n) = Sum_{k=0..n} binomial(k+5,5) * binomial(k,n-k)^2.
5
1, 6, 27, 140, 651, 2772, 11354, 44640, 169371, 624742, 2248575, 7922124, 27397937, 93214632, 312559200, 1034507696, 3384194616, 10954244952, 35118346760, 111602517096, 351819819414, 1100912299156, 3421515852834, 10566654790176, 32441857824859, 99060134392422
OFFSET
0,2
FORMULA
G.f.: (Sum_{k=0..2} A089627(5,k) * (1-x-x^2)^(5-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^(11/2).
PROG
(PARI) a(n) = sum(k=0, n, binomial(k+5, 5)*binomial(k, n-k)^2);
(PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=5, 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