cp's OEIS Frontend

A121630 Finite sum involving signless Stirling numbers of the first kind and the Bell numbers. Appears in the process of normal ordering of n-th power of (a)^3*(a+*a), where a+ and a are boson creation and annihilation operators, respectively.

%I A121630 #11 Mar 14 2014 14:32:24
%S A121630 1,4,29,302,4089,68056,1342949,30635074,792915057,22952573484,
%T A121630 734630159341,25757268041814,981687991859689,40407710444419072,
%U A121630 1786311057929722549,84404172618241446506,4244839086310722228449
%N A121630 Finite sum involving signless Stirling numbers of the first kind and the Bell numbers. Appears in the process of normal ordering of n-th power of (a)^3*(a+*a), where a+ and a are boson creation and annihilation operators, respectively.
%F A121630 a(n)=sum(abs(stirling1(n+1,p))*3^(n-p+1)*bell(p-1),p=1..n+1), n=0,1....
%F A121630 E.g.f.: exp(((1-3*x)^(-1/3))-1)/(1-3*x). - _Vladeta Jovovic_, Aug 13 2006
%F A121630 Recurrence: a(n) = 3*(4*n - 5)*a(n-1) - (54*n^2 - 189*n + 173)*a(n-2) + (108*n^3 - 729*n^2 + 1659*n - 1271)*a(n-3) - 9*(n-3)^2*(3*n - 8)*(3*n - 7)*a(n-4). - _Vaclav Kotesovec_, Mar 14 2014
%F A121630 a(n) ~ 1/2 * 3^(n+7/8) * exp(4*n^(1/4)/3^(3/4) - n - 1) * n^(n+3/8). - _Vaclav Kotesovec_, Mar 14 2014
%t A121630 CoefficientList[Series[E^(((1-3*x)^(-1/3))-1)/(1-3*x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Mar 14 2014 *)
%Y A121630 Cf. A002720, A121629, A121631, A239301.
%K A121630 nonn
%O A121630 0,2
%A A121630 _Karol A. Penson_, Aug 12 2006