cp's OEIS Frontend

A094071 Coefficients arising in combinatorial field theory.

%I A094071 #16 May 19 2025 16:04:24
%S A094071 1,2,10,75,572,6293,92962,1395180,25482135,582310475,13697614020,
%T A094071 364311810217,11551145067139,380339218683310,13636394439014770,
%U A094071 563142483841155427,24264229405883569164,1114389674994185476663
%N A094071 Coefficients arising in combinatorial field theory.
%D A094071 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).
%D A094071 P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G E. H. Duchamp, Combinatorial field theories via boson normal ordering, preprint, Apr 27 2004.
%H A094071 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"
%H A094071 A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, <a href="http://arXiv.org/abs/quant-ph/0409152">A product formula and combinatorial field theory</a>
%F A094071 a(n)=(n+1)!*B(n+1)*[x^(n+1)](exp(x+x^3/3!)), where B(n) are the Bell numbers (A000110) - _Emeric Deutsch_, Nov 23 2004
%p A094071 with(combinat):F:=series(exp(x+x^3/3!),x=0,25): seq((n+1)!*coeff(F,x^(n+1))*bell(n+1),n=0..20);
%t A094071 a[n_] := (n+1)! BellB[n+1] SeriesCoefficient[Exp[x+x^3/3!], {x, 0, n+1}];
%t A094071 Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Nov 11 2018 *)
%Y A094071 Cf. A000085, A005425, A094070, A094072, A094073, A094074.
%Y A094071 Cf. A000110.
%K A094071 nonn
%O A094071 0,2
%A A094071 _N. J. A. Sloane_, May 01 2004
%E A094071 More terms from _Emeric Deutsch_, Nov 23 2004