cp's OEIS Frontend

A094070 a(n) = A000085(n) * A000110(n).

%I A094070 #22 May 19 2025 15:56:26
%S A094070 1,4,20,150,1352,15428,203464,3162960,55405140,1101298600,24222234720,
%T A094070 590544046744,15715973012248,456341011254560,14312979247985120,
%U A094070 484253161428902192,17550722413456774848,680244627812139042016,28053748582811428182080,1228896901162555453603712
%N A094070 a(n) = A000085(n) * A000110(n).
%C A094070 Coefficients arising in combinatorial field theory.
%D A094070 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 A094070 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 A094070 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 A094070 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 A094070 a(n) = (i/sqrt(2))^(n+1)*H(n+1, -i/sqrt(2))*Bell(n+1), where i=sqrt(-1), H(n, x) are the Hermite polynomials and Bell(n) are the Bell numbers. - _Emeric Deutsch_, Nov 22 2004
%p A094070 with(combinat): with(orthopoly): seq((I/sqrt(2))^(n+1)*H(n+1,-I/sqrt(2))*bell(n+1),n=0..17); # _Emeric Deutsch_, Nov 22 2004
%t A094070 a[n_] := Sum[StirlingS1[n+1, k] 2^k BellB[k, 1/2], {k, 0, n+1}] BellB[n+1];
%t A094070 Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Aug 07 2018 *)
%Y A094070 Cf. A000085, A005425, A094071, A094072, A094073, A094074.
%K A094070 nonn
%O A094070 0,2
%A A094070 _N. J. A. Sloane_, May 01 2004
%E A094070 More terms from _Ralf Stephan_, Oct 14 2004