0,2

Main diagonal of array "The first r-Bell numbers" from r=0 and from n=0, p.3 of Mezo. First 7 rows and columns of array shown. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 25 2009]

Istvan Mezo, The r-Bell numbers, Sep 24, 2008. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 25 2009]

a(n) = exp(-1)*Sum_{k>=0} (n+k)^n/k!. E.g.f.: A(x) = exp(-1)*Sum_{k>=0} (1+k*x)^k/k!.

a(n) = Sum_{k=0..n} Stirling1(n,k)*A000110(n+k). [From Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 08 2009]

Contribution from Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 25 2009: (Start)

The array begins:

===================================================

.......|n=0|n=1|.n=2|.n=3.|..n=4.|...n=5.|....n=6.|

r=0....|.1.|.1.|..2.|...5.|...15.|....52.|....203.|

r=1....|.1.|.2.|..5.|..15.|...52.|...203.|....877.|

r=2....|.1.|.3.|.10.|..37.|..151.|...674.|...3263.|

r=3....|.1.|.4.|.17.|..77.|..372.|..1915.|..10481.|

r=4....|.1.|.5.|.26.|.141.|..799.|..4736.|..29371.|

r=5....|.1.|.6.|.37.|.235.|.1540.|.10427.|..73013.|

r=6....|.1.|.7.|.50.|.365.|.2727.|.20878.|.163967.|

===================================================

(End)

with(combinat): a:=proc(n) options operator, arrow: sum(binomial(n, k)*n^(n-k)*bell(k), k=0..n) end proc: 1, seq(a(n), n=1..16); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 02 2008

Sequence in context: A066223 A088500 A095789 this_sequence A098692 A138273 A052568

Adjacent sequences: A134977 A134978 A134979 this_sequence A134981 A134982 A134983

easy,nonn,new

Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 04 2008

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 02 2008