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 A260784 Coefficients in a certain low-temperature series expansion. 1
 0, 24, 1440, 181440, 43545600, 17882726400, 11333177856000, 10257397742592000, 12540115964952576000, 19887027595237490688000, 39679473692005106319360000, 97249082487667949725286400000, 287164491478121796028858368000000, 1005464789964467723115455053824000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Grzegorz Siudem, Agata Fronczak, Bell polynomials in the series expansions of the Ising model, arXiv:2007.16132 [math-ph], 2020. G. Siudem, A. Fronczak, P. Fronczak, Exact low-temperature series expansion for the partition function of the two-dimensional zero-field s= 1/2 Ising model on the infinite square lattice, arXiv preprint arXiv:1410.7963, 2014. See equations (8) and (11). MAPLE A260784 := proc(n)     local a, d1, d2, d3, d4, d33half ;     a := 0 ;     for d2 from 0 do         if 2*d2 > n then             break;         end if;         for d3 from 0 do             if 2*d2 +3*d3 > n then                 break;             end if;             for d4 from 0 do                 if 2*d2 +3*d3+4*d4 > n then                     break;                 end if;                 d1 := n-2*d2-3*d3-4*d4 ;                 if d1 >= 0 and type(d1+d3, 'even') then                     d13half := (d1+d3)/2 ;                     a := a+(d1+d2+d3+d4)!/d1!/d2!/d3!/d4!*(-1)^(d2+d3+d4-1)*2^d2                         /(d1+d2+d3+d4)*binomial(d1+d3, d13half)^2 ;                 end if;             end do:         end do:     end do:     a*n!/2 ; end proc: seq(A260784(2*n), n=1..15) ; # R. J. Mathar, Aug 27 2015 MATHEMATICA "Listing 1" in Siudem et al. (2014) gives Mathematica code for the fractions a(n)/(2n)!) CROSSREFS Cf. A002890. Sequence in context: A187852 A276595 A010797 * A099060 A035174 A288955 Adjacent sequences:  A260781 A260782 A260783 * A260785 A260786 A260787 KEYWORD nonn AUTHOR N. J. A. Sloane, Aug 04 2015 STATUS approved

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Last modified July 24 11:01 EDT 2021. Contains 346273 sequences. (Running on oeis4.)