This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A094072 #26 May 19 2025 16:05:03
%S A094072 1,6,50,615,10192,214571,5544394,171367020,6208928376,259542887975,
%T A094072 12356823485580,662921411131909,39714830070598204,2636484537372437498,
%U A094072 192653800829700013970,15405383160836582657251
%N A094072 Coefficients arising in combinatorial field theory.
%D A094072 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 A094072 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. The title of this paper in the arXiv was later changed to "Some useful combinatorial formulas for bosonic operators"
%F A094072 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 A094072 E.g.f.: exp(-1)*Sum_{k>=0} exp(k*x*exp(k*x))/k!. - _Vladeta Jovovic_, Sep 26 2006
%p A094072 with(combinat): seq(bell(n+1)*sum(k^(n+1-k)*binomial(n+1,k),k=1..n+1),n=0..18);
%t A094072 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 A094072 Cf. A000085, A005425, A094070, A094071, A094073, A094074.
%Y A094072 Cf. A000110.
%K A094072 nonn
%O A094072 0,2
%A A094072 _N. J. A. Sloane_, May 01 2004
%E A094072 More terms from _Emeric Deutsch_, Nov 23 2004