A367415 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^3) ).
1, 1, 2, 5, 15, 52, 198, 793, 3255, 13529, 56696, 239340, 1017900, 4361840, 18828606, 81833505, 357865215, 1573549667, 6952392450, 30848928525, 137403484655, 614104910096, 2753200345000, 12378494389660, 55799811151140, 252141767612812, 1141894552992368
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^4/(1-x)^3))/x) -
PARI
a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n, n-4*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(2*n,n-4*k).