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A377150
a(n) = Sum_{k=0..floor(n/3)} binomial(k+3,3) * binomial(k,n-3*k)^2.
2
1, 0, 0, 4, 4, 0, 10, 40, 10, 20, 180, 180, 55, 560, 1260, 616, 1435, 5600, 5684, 4424, 18956, 33720, 24780, 55944, 147249, 157560, 182280, 523540, 826440, 802560, 1681966, 3531880, 4072035, 5671084, 12941764, 19281064, 22523175, 43823520, 80254746, 99744776
OFFSET
0,4
FORMULA
G.f.: (1-x^3-x^4) * ((1-x^3-x^4)^2 + 6*x^7) / ((1-x^3-x^4)^2 - 4*x^7)^(7/2).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(k+3, 3)*binomial(k, n-3*k)^2);
(PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=3, M=40, x='x+O('x^M), X=1-x^3-x^4, Y=7); Vec(sum(k=0, N\2, a089627(N, k)*X^(N-2*k)*x^(Y*k))/(X^2-4*x^Y)^(N+1/2))
CROSSREFS
Cf. A089627.
Sequence in context: A021698 A199739 A121547 * A028626 A205507 A137862
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 18 2024
STATUS
approved