A367414 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^2) ).
1, 1, 2, 5, 15, 51, 187, 715, 2800, 11138, 44846, 182476, 749566, 3105575, 12966165, 54505650, 230508612, 980045835, 4186600220, 17960356014, 77343359518, 334217730014, 1448771849516, 6298222363395, 27452466169243, 119949953637406, 525284132440963
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)^2))/x) -
PARI
a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n-k, n-4*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(2*n-k,n-4*k).