A138192 A triangular sequence based on expansion of the rational polynomial of A001788 as a Sheffer sequence: p(x,t)=Exp[x*t]*(-1/(2*t - 1)^3).

1, 6, 1, 48, 12, 1, 480, 144, 18, 1, 5760, 1920, 288, 24, 1, 80640, 28800, 4800, 480, 30, 1, 1290240, 483840, 86400, 9600, 720, 36, 1, 23224320, 9031680, 1693440, 201600, 16800, 1008, 42, 1, 464486400, 185794560, 36126720, 4515840, 403200, 26880, 1344

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, May 04 2008

Keywords

• nonn
• uned
• tabl

Comments

Row sums are:

{1, 7, 61, 643, 7993, 114751, 1870837, 34168891, 691354993, 15354462583,371417174701};

Examples

			{1},
{6, 1},
{48, 12, 1},
{480, 144, 18, 1},
{5760, 1920, 288, 24, 1},
{80640, 28800, 4800, 480, 30, 1},
{1290240, 483840, 86400, 9600, 720, 36, 1},
{23224320, 9031680, 1693440, 201600, 16800, 1008, 42, 1},
{464486400, 185794560, 36126720, 4515840, 403200, 26880, 1344, 48, 1}, {10218700800, 4180377600, 836075520, 108380160, 10160640, 725760, 40320,1728,54, 1},
{245248819200, 102187008000, 20901888000, 2786918400, 270950400, 20321280, 1209600, 57600, 2160, 60, 1}
		

Crossrefs

Cf. A001788.

Programs

Mathematica

p[t_] = Exp[x*t]*(-1/(2*t - 1)^3); 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]

Formula

p(x,t)=Exp[x*t]*(-1/(2*t - 1)^3)=Sum(P(x,n)*t^n/n!,{n,0,Infinity}); Out_n,m=n!*Coefficients(P(x,n)).