A372126 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)*(1 + 9*x*A(x))^(1/3) ).
1, 1, 5, 11, 95, 150, 2688, -111, 98489, -215578, 4416842, -18887063, 230670421, -1356589436, 13381147908, -92724422022, 831047516316, -6277471705749, 53925750947589, -426682784513559, 3602138266461603, -29250145766625450, 245524688963062050
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 9^(n-k)*binomial(n+k, k)*binomial(k/3, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 9^(n-k) * binomial(n+k,k) * binomial(k/3,n-k).
From Seiichi Manyama, Nov 30 2024: (Start)
G.f.: exp( Sum_{k>=1} A378555(k) * x^k/k ).
a(n) = (1/(n+1)) * [x^n] 1/(1 - x*(1 + 9*x)^(1/3))^(n+1).
G.f.: (1/x) * Series_Reversion( x*(1 - x*(1 + 9*x)^(1/3)) ). (End)