A381840 G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 - x^2*A(x)^7.
1, 1, 3, 11, 42, 153, 469, 690, -5967, -82708, -700876, -4989894, -32082336, -190742496, -1053280998, -5347579160, -24162468390, -88249158963, -157067396045, 1334548659436, 20996875910808, 194476989681546, 1491599102987040, 10232074769143770, 64440205192609155
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(3*n+k, k)*binomial(4*n-k, n-2*k))/(3*n+1);
Formula
a(n) = (1/(3*n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n+k,k) * binomial(4*n-k,n-2*k).
G.f.: ( (1/x) * Series_Reversion( x * (1-x+x^2)^3 ) )^(1/3).