A094071 Coefficients arising in combinatorial field theory.

1, 2, 10, 75, 572, 6293, 92962, 1395180, 25482135, 582310475, 13697614020, 364311810217, 11551145067139, 380339218683310, 13636394439014770, 563142483841155427, 24264229405883569164, 1114389674994185476663

Offset: 0

Author

N. J. A. Sloane, May 01 2004

Keywords

• nonn

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

• P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Combinatorial field theories via boson normal ordering, 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"
• A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, A product formula and combinatorial field theory

Crossrefs

Cf. A000085, A005425, A094070, A094072, A094073, A094074.

Cf. A000110.

Programs

Maple

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);

Mathematica

a[n_] := (n+1)! BellB[n+1] SeriesCoefficient[Exp[x+x^3/3!], {x, 0, n+1}];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Nov 11 2018 *)

Formula

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

Extensions

More terms from Emeric Deutsch, Nov 23 2004