A378610 Expansion of (1/x) * Series_Reversion( x * (1 - x/(1 - x))^4 ).
1, 4, 30, 276, 2825, 30884, 353108, 4170500, 50485764, 623084056, 7810707894, 99175174284, 1272856327470, 16486135484248, 215212582153840, 2828658852385572, 37401956484705132, 497174193516767600, 6640063367021736728, 89058042321373540912, 1199031374607501831273
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x/(1-x))^4)/x) -
PARI
a(n, s=1, t=4, u=-4) = 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
G.f.: exp( Sum_{k>=1} A378613(k) * x^k/k ).
a(n) = (1/(n+1)) * [x^n] 1/(1 - x/(1 - x))^(4*(n+1)).
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(n-1,n-k).
G.f.: B(x)^4 where B(x) is the g.f. of A243667.
a(n) = 4 * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(n,k) * binomial(4*n+k+4,n)/(4*n+k+4).