A094070 - OEIS

%I #20 Oct 09 2023 11:18:32

%S 1,4,20,150,1352,15428,203464,3162960,55405140,1101298600,24222234720,

%T 590544046744,15715973012248,456341011254560,14312979247985120,

%U 484253161428902192,17550722413456774848,680244627812139042016,28053748582811428182080,1228896901162555453603712

%N a(n) = A000085(n) * A000110(n).

%C 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) = (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 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 a[n_] := Sum[StirlingS1[n+1, k] 2^k BellB[k, 1/2], {k, 0, n+1}] BellB[n+1];

%t Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Aug 07 2018 *)

%Y Cf. A000085, A005425, A094071, A094072, A094073, A094074.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, May 01 2004

%E More terms from _Ralf Stephan_, Oct 14 2004