A387092 Expansion of B(x)/sqrt(1 + 8*(B(x)-1)/9), where B(x) is the g.f. of A169958.
1, 5, 73, 1273, 23993, 472483, 9570669, 197720403, 4144499289, 87850211830, 1878702271039, 40466493877812, 876838997392189, 19095109351916182, 417622272948538767, 9167498552774475792, 201891862924784199321, 4458815817948146064915
Offset: 0
Keywords
Programs
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Mathematica
nmax = 25; CoefficientList[Series[Sum[Binomial[9*n, n]*x^n, {n, 0, nmax}] / Sqrt[1 + 8*(Sum[Binomial[9*n, n]*x^n, {n, 0, nmax}] - 1)/9], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 20 2025 *)
Formula
Sum_{k=0..n} a(k) * a(n-k) = A387091(n).
G.f.: 1/sqrt(1 - x*g^7*(9+g)) where g = 1+x*g^9 is the g.f. of A062994.
G.f.: g/sqrt(9-8*g) where g = 1+x*g^9 is the g.f. of A062994.
a(n) ~ 3^(18*n + 3/2) / (Gamma(1/4) * n^(3/4) * 2^(24*n + 5/2)). - Vaclav Kotesovec, Aug 20 2025