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 A094070 a(n) = A000085(n) * A000110(n). 3
 1, 4, 20, 150, 1352, 15428, 203464, 3162960, 55405140, 1101298600, 24222234720, 590544046744, 15715973012248, 456341011254560, 14312979247985120, 484253161428902192, 17550722413456774848, 680244627812139042016, 28053748582811428182080, 1228896901162555453603712 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Coefficients arising in combinatorial field theory. REFERENCES 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). 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. LINKS Table of n, a(n) for n=0..19. P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Combinatorial field theories via boson normal ordering A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, A product formula and combinatorial field theory FORMULA 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 MAPLE 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 MATHEMATICA a[n_] := Sum[StirlingS1[n+1, k] 2^k BellB[k, 1/2], {k, 0, n+1}] BellB[n+1]; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Aug 07 2018 *) CROSSREFS Cf. A000085, A005425, A094071, A094072, A094073, A094074. Sequence in context: A001171 A247331 A167018 * A335627 A119022 A006682 Adjacent sequences: A094067 A094068 A094069 * A094071 A094072 A094073 KEYWORD nonn AUTHOR N. J. A. Sloane, May 01 2004 EXTENSIONS More terms from Ralf Stephan, Oct 14 2004 STATUS approved

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Last modified June 16 16:46 EDT 2024. Contains 373432 sequences. (Running on oeis4.)