A308517 Expansion of e.g.f. exp(1 - exp(x/(1 - x))).

1, -1, -2, -5, -11, 18, 711, 10113, 125042, 1485627, 17151083, 185932580, 1665928529, 4570649471, -349942007986, -14532197609433, -433111168649251, -11579368513540914, -293948221716443209, -7208510256850719447, -170577027262193604678, -3823168355141657356481, -76959686241473750407701

Offset

0,3

Comments

Lah transform of A000587 (complementary Bell numbers).

Links

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

Formula

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

Mathematica

nmax = 22; CoefficientList[Series[Exp[1 - Exp[x/(1 - x)]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] BellB[k, -1] n!/k!, {k, 0, n}]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A000587, A084357.

Sequence in context: A260037 A132455 A132459 * A375714 A101057 A045362

Adjacent sequences: A308514 A308515 A308516 * A308518 A308519 A308520

Keyword

sign

Author

Ilya Gutkovskiy, Jun 03 2019

Status

approved