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A293037 E.g.f.: exp(1 + x - exp(x)). 14
1, 0, -1, -1, 2, 9, 9, -50, -267, -413, 2180, 17731, 50533, -110176, -1966797, -9938669, -8638718, 278475061, 2540956509, 9816860358, -27172288399, -725503033401, -5592543175252, -15823587507881, 168392610536153, 2848115497132448, 20819319685262839 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..593

FORMULA

a(n) = exp(1) * Sum_{k>=0} (-1)^k*(k + 1)^n/k!. - Ilya Gutkovskiy, Jun 13 2019

a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k, -1). - Vaclav Kotesovec, Jul 06 2020

MAPLE

f:= series(exp(1 + x - exp(x)), x= 0, 101): seq(factorial(n) * coeff(f, x, n), n = 0..30); # Muniru A Asiru, Oct 31 2017

MATHEMATICA

m = 26; Range[0, m]! * CoefficientList[Series[Exp[1 + x - Exp[x]], {x, 0, m}], x] (* Amiram Eldar, Jul 06 2020 *)

Table[Sum[Binomial[n, k] * BellB[k, -1], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 06 2020 *)

PROG

(PARI) x='x+O('x^66); Vec(serlaplace(exp(-exp(x)+1+x)))

CROSSREFS

Column k=1 of A293051.

Column k=1 of A335977.

Cf. A000587 (k=0), this sequence (k=1), A293038 (k=2), A293039 (k=3), A293040 (k=4).

Cf. A000296, A014182.

Sequence in context: A109322 A000587 A014182 * A131463 A065644 A043065

Adjacent sequences:  A293034 A293035 A293036 * A293038 A293039 A293040

KEYWORD

sign

AUTHOR

Seiichi Manyama, Sep 28 2017

STATUS

approved

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Last modified May 7 05:10 EDT 2021. Contains 343636 sequences. (Running on oeis4.)