|
%I #14 Oct 09 2023 11:18:59
%S 1,2,10,75,572,6293,92962,1395180,25482135,582310475,13697614020,
%T 364311810217,11551145067139,380339218683310,13636394439014770,
%U 563142483841155427,24264229405883569164,1114389674994185476663
%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).
%D 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 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>
%H 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 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 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 a[n_] := (n+1)! BellB[n+1] SeriesCoefficient[Exp[x+x^3/3!], {x, 0, n+1}];
%t Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Nov 11 2018 *)
%Y Cf. A000085, A005425, A094070, A094072, 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
|
