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

0,2

Links

Table of n, a(n) for n=0..17.

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 A059967.

G.f.: g/sqrt(9-8*g) where g = 1+x*g^9 is the g.f. of A059967.

a(n) ~ 3^(18*n + 3/2) / (Gamma(1/4) * n^(3/4) * 2^(24*n + 5/2)). - Vaclav Kotesovec, Aug 20 2025

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 *)

Crossrefs

Cf. A226706, A383965.

Cf. A059967, A169958, A387091.

Sequence in context: A155662 A182328 A222352 * A159509 A127167 A378409

Adjacent sequences: A387089 A387090 A387091 * A387093 A387094 A387095

Keyword

nonn

Author

Seiichi Manyama, Aug 16 2025

Status

approved