A375470 a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(k,n-3*k)^2.
1, 0, 0, 2, 2, 0, 3, 12, 3, 4, 36, 36, 9, 80, 180, 86, 155, 600, 607, 402, 1581, 2808, 1967, 3780, 9816, 10376, 10584, 28626, 44918, 41184, 77627, 160436, 181044, 228972, 499512, 735654, 811823, 1467072, 2640231, 3191642, 4494502, 8566308, 12280547, 15315974, 26498718
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, (k+1)*binomial(k, n-3*k)^2);
Formula
G.f.: (1-x^3-x^4)/((1-x^3-x^4)^2 - 4*x^7)^(3/2).