A369212 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^3) ).
1, 2, 5, 15, 50, 177, 652, 2473, 9594, 37892, 151846, 615859, 2523217, 10427471, 43415259, 181941198, 766841846, 3248517320, 13823977350, 59067577266, 253315964424, 1089998388418, 4704475230340, 20361365646315, 88351705071583, 384280788724692, 1675063399090659
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^3))/x) -
PARI
a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(2*n-2*k+2, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(2*n-2*k+2,n-3*k).