A094073
Coefficients arising in combinatorial field theory.
Original entry on oeis.org
4, 240, 49938, 24608160, 23465221750, 38341895571708, 98780305524248572, 377796303580335320432, 2048907276496726375662702, 15198414983297581845761672560, 149768511689247547252666676150490
Offset: 1
- Vincenzo Librandi, Table of n, a(n) for n = 1..160
- 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"
- 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).
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with(combinat): a:=n->bell(2*n)*(2*n)!*coeff(series(exp(x*sinh(x)), x=0,40), x^(2*n)): seq(a(n),n=1..13); # Emeric Deutsch, Jan 22 2005
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a[n_] := (2n)! BellB[2n] SeriesCoefficient[Exp[x Sinh[x]], {x, 0, 2n}];
Table[a[n], {n, 1, 11}] (* Jean-François Alcover, Nov 11 2018 *)
A094071
Coefficients arising in combinatorial field theory.
Original entry on oeis.org
1, 2, 10, 75, 572, 6293, 92962, 1395180, 25482135, 582310475, 13697614020, 364311810217, 11551145067139, 380339218683310, 13636394439014770, 563142483841155427, 24264229405883569164, 1114389674994185476663
Offset: 0
- 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.
- 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
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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);
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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 *)
A094072
Coefficients arising in combinatorial field theory.
Original entry on oeis.org
1, 6, 50, 615, 10192, 214571, 5544394, 171367020, 6208928376, 259542887975, 12356823485580, 662921411131909, 39714830070598204, 2636484537372437498, 192653800829700013970, 15405383160836582657251
Offset: 0
- 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, 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"
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with(combinat): seq(bell(n+1)*sum(k^(n+1-k)*binomial(n+1,k),k=1..n+1),n=0..18);
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Table[BellB[n+1]Sum[Binomial[n+1,k]k^(n+1-k),{k,n+1}],{n,0,20}] (* Harvey P. Dale, Feb 05 2015 *)
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