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

0,2

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..17.

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)=(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

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 *)

Crossrefs

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

Cf. A000110.

Sequence in context: A005365 A191812 A059104 * A358437 A289679 A352270

Adjacent sequences: A094068 A094069 A094070 * A094072 A094073 A094074

Keyword

nonn

Author

N. J. A. Sloane, May 01 2004

Extensions

More terms from Emeric Deutsch, Nov 23 2004

Status

approved