A372537 G.f. A(x) satisfies A(A(A(A(x)))) = x + 4*x^2 + 16*x^3.

0, 1, 1, 1, -15, 81, -159, -1695, 19857, -77775, -372351, 6628545, -24096975, -232640751, 2756221601, 2199811873, -210934282287, 553408050417, 17722961332929, -95716389015423, -1950283855292559, 15527782649242065, 285278599792984545, -3006768595808218911

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..486

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) = 1/4 * ( 4^(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) * b(j,k)) * b(k,l)) * b(l,m) ). a(n) = b(n,1).

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

B(B(x)) = x + 4*x^2 + 16*x^3.

B(x) = F(2*x)/2, where F(x) is the g.f. for A220110.

Example

A(A(x)) = x + 2*x^2 + 4*x^3 - 24*x^4 + 80*x^5 + 32*x^6 - 2496*x^7 + 14976*x^8 + ...

Crossrefs

Cf. A220110, A220288, A371841, A372521.

Sequence in context: A244855 A102360 A375998 * A344722 A309336 A266288

Adjacent sequences: A372534 A372535 A372536 * A372538 A372539 A372540

Keyword

sign

Author

Seiichi Manyama, May 05 2024

Status

approved