A137943 This sequence needs a proper definition.

-1, 0, -1, -6, 0, -1, -12, -18, 0, -1, -216, -48, -36, 0, -1, -1440, -1080, -120, -60, 0, -1, -22320, -8640, -3240, -240, -90, 0, -1, -272160, -156240, -30240, -7560, -420, -126, 0, -1, -4717440, -2177280, -624960, -80640, -15120, -672, -168, 0, -1, -81285120, -42456960, -9797760, -1874880, -181440

Offset

1,4

Comments

Previous name was: Triangle of coefficients associate with the expansion of the K_3 graph matrix characteristic polynomial as a Sheffer sequence: M = {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}} f(t)=-t^3+3t+2 p(x,t)=Exp[x,t)/(2*t^3+3*t^2-1)=exp(x*t)(t^3*f(1/t)).

References

Jonathan L. Gross and Thomas W. Tucker," Topological Graph Theory",Dover, New York,2001, page 10 figure 1.7

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 149

Links

Table of n, a(n) for n=1..50.

Example

{-1},
{0, -1},
{-6, 0, -1},
{-12, -18, 0, -1},
{-216, -48, -36, 0, -1},
{-1440, -1080, -120, -60, 0, -1},
{-22320, -8640, -3240, -240, -90, 0, -1},
{-272160, -156240, -30240, -7560, -420, -126, 0, -1},
{-4717440, -2177280, -624960, -80640, -15120, -672, -168, 0, -1},
{-81285120, -42456960, -9797760, -1874880, -181440, -27216, -1008, -216, 0, -1},
{-1665619200, -812851200, -212284800, -32659200, -4687200, -362880, -45360, -1440, -270, 0, -1}

Mathematica

(*K_3 graph connection matrix*) M = {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}};
f[t_] = CharacteristicPolynomial[M, t];
p[t_] = ExpandAll[Exp[x*t]/(t^3*f[1/t])];
g = Table[ExpandAll[(n!)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}];
a = Table[ CoefficientList[(n!)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];
Flatten[a]

Crossrefs

Sequence in context: A195445 A215080 A317446 * A202189 A202183 A227612

Adjacent sequences: A137940 A137941 A137942 * A137944 A137945 A137946

Keyword

tabl,uned,sign

Author

Roger L. Bagula, Apr 30 2008

Status

approved