A154923 A symmetrical triangle sequence made from A154537:q(x,n)= Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]); p(x,n)=q(x,n)+x^n*q(1/x,n); t(n,m)=coefficients(p(x,n)).

2, 3, 3, 5, 16, 5, 9, 62, 62, 9, 17, 208, 464, 208, 17, 33, 642, 2680, 2680, 642, 33, 65, 1880, 13404, 24320, 13404, 1880, 65, 129, 5322, 62188, 180488, 180488, 62188, 5322, 129, 257, 14752, 280144, 1209600, 1858752, 1209600, 280144, 14752, 257, 513

Offset: 0

Author

Roger L. Bagula, Jan 17 2009

Keywords

• nonn
• tabl
• uned

Comments

Row sums are:

{2, 6, 26, 142, 914, 6710, 55018, 496254, 4868258, 51483878, 582795578,...}

Examples

			{2},
{3, 3},
{5, 16, 5},
{9, 62, 62, 9},
{17, 208, 464, 208, 17},
{33, 642, 2680, 2680, 642, 33},
{65, 1880, 13404, 24320, 13404, 1880, 65},
{129, 5322, 62188, 180488, 180488, 62188, 5322, 129},
{257, 14752, 280144, 1209600, 1858752, 1209600, 280144, 14752, 257},
{513, 40418, 1262544, 7828640, 16609824, 16609824, 7828640, 1262544, 40418, 513},
{1025, 110248, 5787604, 50950400, 140957728, 187181568, 140957728, 50950400, 5787604, 110248, 1025}
		

Crossrefs

A154537

Programs

Mathematica

p[x_, n_] = Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]);
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}]'
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]
+ Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}]'
Flatten[%]

Formula

q(x,n)= Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]);

p(x,n)=q(x,n)+x^n*q(1/x,n);

t(n,m)=coefficients(p(x,n)).