A372499 G.f. satisfies A(A(A(x))) = F(x), where F(x) is the g.f. for A053540(n) = n*9^(n-1).

0, 1, 6, 9, 54, 0, -1944, 44469, -323676, -5990193, 179194032, 484654509, -105337511100, 757846026261, 85419734244300, -1707846638480514, -90276038133498612, 3464956887464464164, 118426852966952180502, -7984363576091338944720, -181143285020960488524558

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..200

Formula

Define the sequence b(n,m) as follows. If n<m, b(n,m) = 0, else if n=m, b(n,m) = 1, otherwise b(n,m) = 1/3 * ( 9^(n-m) * binomial(n+m-1,2*m-1) - Sum_{l=m+1..n-1} (b(n,l) + Sum_{k=l..n} b(n,k) * b(k,l)) * b(l,m) ). a(n) = b(n,1).

Example

A(A(x)) = x + 12*x^2 + 90*x^3 + 594*x^4 + 3807*x^5 + 20412*x^6 + 123201*x^7 + 1032264*x^8 - 1463103*x^9 - 35468766*x^10 + ...

Crossrefs

Cf. A309509, A372492.

Cf. A053540, A141118, A372500.

Sequence in context: A187998 A177181 A126110 * A340819 A254207 A098662

Adjacent sequences: A372496 A372497 A372498 * A372500 A372501 A372502

Keyword

sign

Author

Seiichi Manyama, May 03 2024

Status

approved