A369592 Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)^3) ).
1, 1, 1, 1, 2, 3, 4, 5, 10, 16, 23, 31, 62, 102, 152, 213, 426, 712, 1084, 1556, 3112, 5255, 8116, 11843, 23686, 40288, 62866, 92842, 185684, 317548, 499376, 744277, 1488554, 2556376, 4044740, 6072124, 12144248, 20926236, 33272912, 50244660, 100489320, 173634752
Offset: 0
Keywords
Programs
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PARI
my(N=50, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^4/(1+x)^3))/x) -
PARI
a(n) = sum(k=0, n\4, (n-4*k+1)*binomial(n+1, k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n-4*k+1) * binomial(n+1,k).
Comments