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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

Table of n, a(n) for n=1..14.

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.)