A367413 Expansion of (1/x) * Series_Reversion( x * (1-x-x^3/(1-x)^2) ).
1, 1, 2, 6, 22, 87, 356, 1493, 6398, 27936, 123906, 556734, 2528668, 11590555, 53545932, 249065874, 1165482126, 5482782933, 25914899804, 123009541412, 586121731150, 2802470267460, 13441993044464, 64660400422341, 311861855749484, 1507802756171072, 7306422899878394
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^3/(1-x)^2))/x) -
PARI
a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(2*n,n-3*k).
From Seiichi Manyama, Nov 27 2024: (Start)
G.f.: exp( Sum_{k>=1} A378464(k) * x^k/k ).
a(n) = (1/(n+1)) * [x^n] 1/(1 - x - x^3/(1 - x)^2)^(n+1). (End)