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%I #24 Oct 09 2023 11:19:08
%S 1,6,50,615,10192,214571,5544394,171367020,6208928376,259542887975,
%T 12356823485580,662921411131909,39714830070598204,2636484537372437498,
%U 192653800829700013970,15405383160836582657251
%N Coefficients arising in combinatorial field theory.
%D P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Some useful combinatorial formulas for bosonic operators, J. Math. Phys. 46, 052110 (2005) (6 pages).
%H P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, <a href="http://arXiv.org/abs/quant-ph/0405103">Combinatorial field theories via boson normal ordering</a>, arXiv:quant-ph/0405103, 2004-2006.
%F a(n) = B(n+1)*Sum_{k=1..n+1} binomial(n+1, k)*k^(n+1-k), where B(n) are the Bell numbers (A000110). - _Emeric Deutsch_, Nov 23 2004
%F E.g.f.: exp(-1)*Sum_{k>=0} exp(k*x*exp(k*x))/k!. - _Vladeta Jovovic_, Sep 26 2006
%p with(combinat): seq(bell(n+1)*sum(k^(n+1-k)*binomial(n+1,k),k=1..n+1),n=0..18);
%t Table[BellB[n+1]Sum[Binomial[n+1,k]k^(n+1-k),{k,n+1}],{n,0,20}] (* _Harvey P. Dale_, Feb 05 2015 *)
%Y Cf. A000085, A005425, A094070, A094071, A094073, A094074.
%Y Cf. A000110.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 01 2004
%E More terms from _Emeric Deutsch_, Nov 23 2004