A308518 Expansion of e.g.f. exp(1 - exp(1 - exp(x))).

1, 1, 1, 0, -4, -12, -3, 150, 744, 525, -16799, -118280, -148289, 4036802, 37244157, 68676153, -1758280309, -20207442595, -49855713746, 1245931950070, 17250366460410, 53991885230741, -1330935478357842, -21705274324058996, -83339285813776419, 2026672671500822591, 38327819123289163864

Offset: 0

Author

Ilya Gutkovskiy, Jun 03 2019

Keywords

• sign

Crossrefs

Cf. A000258, A000587, A130410, A308519.

Programs

Mathematica

nmax = 26; CoefficientList[Series[Exp[1 - Exp[1 - Exp[x]]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k StirlingS2[n, k] BellB[k, -1], {k, 0, n}], {n, 0, 26}]
a[n_] := a[n] = -Sum[Binomial[n - 1, k - 1] BellB[k, -1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 26}]

Formula

a(n) = Sum_{k=0..n} (-1)^k*Stirling2(n,k)*A000587(k).

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1)*A000587(k)*a(n-k).