A371435 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + x^4) ).
1, 3, 15, 91, 611, 4368, 32590, 250821, 1976441, 15865465, 129275835, 1066438399, 8888818659, 74743312480, 633272709348, 5400983817990, 46330852036920, 399479717666693, 3460229824525809, 30095179524446946, 262722158090170570, 2301201197665717770
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3+x^4))/x) -
PARI
a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, k)*binomial(4*n-k+2, n-4*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+k,k) * binomial(4*n-k+2,n-4*k).