A387091 a(n) = binomial(9*n+1,n).

1, 10, 171, 3276, 66045, 1370754, 28989675, 621216192, 13442126049, 293052087900, 6426898010533, 141629804643600, 3133614810784185, 69566517009302868, 1548833316392624625, 34569147570568156800, 773240476721553042345, 17328840976366636057110

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..700

Formula

a(n) = Sum_{k=0..n} binomial(9*n-k,n-k).

G.f.: 1/(1 - x*g^7*(9+g)) where g = 1+x*g^9 is the g.f. of A059967.

G.f.: g^2/(9-8*g) where g = 1+x*g^9 is the g.f. of A059967.

G.f.: B(x)^2/(1 + 8*(B(x)-1)/9), where B(x) is the g.f. of A169958.

D-finite with recurrence +128*n*(8*n-5)*(4*n-1)*(8*n+1)*(2*n-1)*(8*n-1)*(4*n-3)*(8*n-3)*a(n) -81*(9*n-7)*(9*n-5)*(3*n-1)*(9*n-1)*(9*n+1)*(3*n-2)*(9*n-4)*(9*n-2)*a(n-1)=0. - R. J. Mathar, Aug 19 2025

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

Mathematica

A387091[n_] := Binomial[9*n + 1, n]; Array[A387091, 20, 0] (* Paolo Xausa, Aug 20 2025 *)

Prog

(PARI) a(n) = binomial(9*n+1, n);

Crossrefs

Cf. A001700, A045721, A052203, A079589, A079590.

Cf. A059967, A169958.

Sequence in context: A187204 A346458 A133273 * A239763 A387930 A112703

Adjacent sequences: A387088 A387089 A387090 * A387092 A387093 A387094

Keyword

nonn,easy

Author

Seiichi Manyama, Aug 16 2025

Status

approved