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A121631 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)^4*(a+*a), where a+ and a are boson creation and annihilation operators, respectively.

%I A121631 #13 Mar 14 2014 14:32:51
%S A121631 1,5,46,613,10679,229576,5868715,173833661,5853205468,220767370219,
%T A121631 9219128625851,422221005543250,21041188313139901,1133454896301865073,
%U A121631 65627299232007207934,4064319309355535125201,268077821490093243979235
%N A121631 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)^4*(a+*a), where a+ and a are boson creation and annihilation operators, respectively.
%F A121631 a(n)=sum(abs(stirling1(n+1,p))*4^(n-p+1)*bell(p-1),p=1..n+1), n=0,1....
%F A121631 E.g.f.: exp(((1-4*x)^(-1/4))-1)/(1-4*x). - _Vladeta Jovovic_, Aug 13 2006
%F A121631 Recurrence: a(n) = 2*(10*n - 17)*a(n-1) - (160*n^2 - 704*n + 811)*a(n-2) + 2*(320*n^3 - 2592*n^2 + 7138*n - 6675)*a(n-3) - (1280*n^4 - 16384*n^3 + 79120*n^2 - 170816*n + 139079)*a(n-4) + 32*(n-4)^2*(2*n - 7)*(4*n - 15)*(4*n - 13)*a(n-5). - _Vaclav Kotesovec_, Mar 14 2014
%F A121631 a(n) ~ 1/sqrt(5) * 2^(2*n+9/5) * exp(5*n^(1/5)/2^(8/5)-n-1) * n^(n+2/5). - _Vaclav Kotesovec_, Mar 14 2014
%t A121631 CoefficientList[Series[E^(((1-4*x)^(-1/4))-1)/(1-4*x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Mar 14 2014 *)
%Y A121631 Cf. A002720, A121629, A121630, A239301.
%K A121631 nonn
%O A121631 0,2
%A A121631 _Karol A. Penson_, Aug 12 2006