A372795 E.g.f. A(x) satisfies A(A(A(A(x)))) = (exp(8*x) - 1)/8.

0, 1, 2, -2, 8, 24, -2240, 59600, -640000, -35477120, 2287843200, -337824000, -8328489693696, 320219485774848, 53149588906171392, -5832590252624818176, -534898113615540043776, 142559169839206640025600, 6582786304965587026329600

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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 * ( 8^(n-m) * Stirling2(n,m) - 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).

Crossrefs

Cf. A184011, A209519, A372746.

Cf. A372796.

Sequence in context: A054093 A098557 A354066 * A287756 A287496 A003616

Adjacent sequences: A372792 A372793 A372794 * A372796 A372797 A372798

Keyword

sign

Author

Seiichi Manyama, May 13 2024

Status

approved