A369503 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^2)^2 ).
1, 4, 24, 168, 1284, 10384, 87360, 756704, 6703168, 60444928, 552990592, 5120101760, 47887472000, 451759449600, 4293634467840, 41073654689280, 395170166443008, 3821262491103232, 37118973530660864, 362035991963869184, 3544080121528001536
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^2)^2)/x) -
PARI
a(n) = sum(k=0, n\2, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-2*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(4*n-2*k+4,n-2*k).