A378426 Expansion of (1/x) * Series_Reversion( x / (1 + x + x^2 * (1 + x)^2) ).
1, 1, 2, 6, 18, 56, 184, 624, 2161, 7621, 27283, 98869, 361967, 1336843, 4974763, 18634683, 70207751, 265874119, 1011475368, 3863846328, 14814818017, 56994831109, 219941836172, 851138940402, 3302281633591, 12842844277471, 50056915575566, 195503017533502
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^2*(1+x)^2))/x) -
PARI
a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(n+k+1, n-2*k))/(n+1);
Formula
G.f.: exp( Sum_{k>=1} A378405(k) * x^k/k ).
a(n) = (1/(n+1)) * [x^n] (1 + x + x^2 * (1 + x)^2)^(n+1).
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(n+k+1,n-2*k).