A393790 Expansion of e.g.f. (exp(exp(2*x) - 1) + 1) / 2.

1, 1, 4, 20, 120, 832, 6496, 56128, 529920, 5413632, 59379200, 694855680, 8629446656, 113231613952, 1563847245824, 22658392801280, 343413297872896, 5430632107474944, 89401171136872448, 1529018372602462208, 27118355472906715136, 497937092346381336576, 9451267924316280324096

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = 2^(n-1) * Bell(n) for n > 0.

a(n) = Sum_{k=0..n} Stirling2(n,k) * A000902(k).

a(n) ~ 2^(n-1) * n^n / (sqrt(1 + LambertW(n)) * exp(n + 1 - n/LambertW(n)) * LambertW(n)^n). - Vaclav Kotesovec, Feb 27 2026

a(n) = A055882(n)/2 for n>0. - Hugo Pfoertner, Feb 28 2026

Mathematica

nmax = 22; CoefficientList[Series[(Exp[Exp[2 x] - 1] + 1)/2, {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[2^(n - 1) BellB[n], {n, 1, 22}]]

Crossrefs

Cf. A000110, A000902, A011782, A055882, A217486.

Sequence in context: A093123 A092055 A386708 * A187848 A370653 A001715

Adjacent sequences: A393786 A393787 A393789 * A393791 A393792 A393793

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 27 2026

Status

approved