A371841 G.f. A(x) satisfies A(A(A(A(A(A(x)))))) = x + 6*x^2 + 36*x^3.

0, 1, 1, 1, -35, 325, -1295, -12455, 283285, -2186675, -5612255, 324564625, -2869315163, -12271744331, 490525545169, -2159646628535, -58485623789483, 634417586418781, 8780962428445537, -156001827155519807, -2145519156372933275, 50455156500263955781

Offset

0,5

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) = 1/6 * ( 6^(n-m) * Sum_{l=0..m} binomial(l,n-3*m+2*l) * binomial(m,l) - Sum_{l=m+1..n-1} (b(n,l) + Sum_{k=l..n} (b(n,k) + Sum_{j=k..n} (b(n,j) + Sum_{i=j..n} (b(n,i) + Sum_{h=i..n} b(n,h) * b(h,i)) * b(i,j)) * b(j,k)) * b(k,l)) * b(l,m) ). a(n) = b(n,1).

Let B(x) = A(A(x)) and C(x) = A(A(A(x))).

B(B(B(x))) = C(C(x)) = x + 6*x^2 + 36*x^3.

B(x) = F(2*x)/2, where F(x) is the g.f. for A220288.

C(x) = G(3*x)/3, where G(x) is the g.f. for A220110.

Example

A(A(x)) = x + 2*x^2 + 4*x^3 - 64*x^4 + 448*x^5 - 832*x^6 - 24704*x^7 + ...
A(A(A(x))) = x + 3*x^2 + 9*x^3 - 81*x^4 + 405*x^5 + 243*x^6 - 28431*x^7 + ...

Crossrefs

Cf. A220110, A220288, A372521, A372537.

Sequence in context: A220924 A220995 A264488 * A227058 A372151 A027792

Adjacent sequences: A371838 A371839 A371840 * A371842 A371843 A371844

Keyword

sign

Author

Seiichi Manyama, May 04 2024

Status

approved