A376326 Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^4 ).
1, 4, 30, 272, 2737, 29380, 329614, 3818540, 45329440, 548511612, 6740687924, 83898110660, 1055441468145, 13398494365088, 171422870731600, 2208161418665872, 28614197357895055, 372754395074051500, 4878709294080115494, 64123505084010848580, 846018700129069313495
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^4)/x) -
PARI
a(n, s=2, t=4, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(4*n+k+3,k) * binomial(5*n-k+3,n-2*k).
G.f.: B(x)^4, where B(x) is the g.f. of A365188.