A177429 Triangle read by rows: T(n,m)=A060187(1+n,1+m) *n! / (n-m)!

1, 1, 1, 1, 12, 2, 1, 69, 138, 6, 1, 304, 2760, 1824, 24, 1, 1185, 33640, 100920, 28440, 120, 1, 4332, 316290, 2825760, 3795480, 519840, 720, 1, 15253, 2547594, 54541830, 218167320, 152855640, 10982160, 5040, 1, 52416, 18570272, 835056768

Offset: 0

Author

Roger L. Bagula, May 08 2010

Keywords

• nonn
• tabl
• easy

Comments

Row sums are: 1, 2, 15, 214, 4913, 164306, 7462423, 439114838, 32358353217, 2909210035042, 312597121198751,...

Examples

			1;
1, 1;
1, 12, 2;
1, 69, 138, 6;
1, 304, 2760, 1824, 24;
1, 1185, 33640, 100920, 28440, 120;
1, 4332, 316290, 2825760, 3795480, 519840, 720;
1, 15253, 2547594, 54541830, 218167320, 152855640, 10982160, 5040;
1, 52416, 18570272, 835056768, 7854023520, 16701135360, 6685297920, 264176640, 40320;
1, 177057, 126456480, 10940817888, 209905801056, 1049529005280, 1312898146560, 318670329600, 7138938240, 362880;
		

Crossrefs

Cf. A060187

Programs

Maple

A177429 := proc(n,k)
    A060187(n+1,k+1)*n!/(n-k)! ;
end proc: # R. J. Mathar, Jun 16 2015

Mathematica

(*A060187*);
p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];
f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
t[n_, m_] := f[n, m]*n!/(n - m)!;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]