A039764 D-analogs of Bell numbers.

1, 1, 4, 15, 72, 403, 2546, 17867, 137528, 1149079, 10335766, 99425087, 1017259964, 11018905667, 125860969266, 1510764243699, 18999827156304, 249687992188015, 3420706820299374, 48751337014396167

Offset: 0

Author

Ruedi Suter (suter(AT)math.ethz.ch)

Keywords

• nonn

Links

• Hasan Arslan, Nazmiye Alemdar, Mariam Zaarour, and Hüseyin Altındiş, On Bell numbers of type D, arXiv:2504.16522 [math.CO], 2025. See p. 4.
• Ruedi Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.

Crossrefs

B-analogs of Bell numbers = A007405.

Programs

Mathematica

Range[0, 25]! CoefficientList[Series[(Exp[x] - x) Exp[1/2 (Exp[2 x] - 1)], {x, 0, 25}], x] (* Vincenzo Librandi, May 03 2015 *)

PARI

x='x+O('x^30); Vec(serlaplace((exp(x) - x)*exp(1/2*(exp(2*x) - 1)))) \\ Michel Marcus, May 03 2015

Formula

E.g.f.: (exp(x) - x)*exp(1/2*(exp(2*x) - 1)).

a(n) = Sum_{k=0..n} A039760(n, k).