A216379 Triangle of generalized Stirling numbers S_{n,n}(5,k) read by rows (n>=0, n<=k<=5n) the sum of which is A182924.

1, 1, 15, 25, 10, 1, 16, 1280, 9080, 16944, 12052, 3840, 580, 40, 1, 1296, 330480, 6148872, 28245672, 49658508, 41392620, 18428400, 4691412, 706833, 63375, 3285, 90, 1, 331776, 207028224, 8190885888, 74684104704, 253100173824, 405044582400, 351783415296, 181005401088, 58436640576, 12288192000, 1721191680, 162115584, 10228144, 423360, 10960, 160, 1

Offset: 0

Author

Jean-François Alcover, Sep 06 2012

Keywords

• nonn
• tabf
• easy

Examples

			{1},
{1,15,25,10,1},
{16,1280,9080,16944,12052,3840,580,40,1}
...
		

Crossrefs

Cf. A182924.

Second row (n=1) is 5th row of A008277 (Stirling numbers S2).

Third row is 5th row of A078739 (Generalized Stirling numbers S_{2,2}).

Fourth row is 5th row of A078741 (Generalized Stirling numbers S_{3,3}).

Fifth row is 5th row of A090214 (Generalized Stirling numbers S_{4,4}).

Programs

Mathematica

f[m_][n_, k_] := (-1)^k/k!*Sum[(-1)^p*Binomial[k, p]*FactorialPower[p, m]^n, {p, m, k}]; Table[f[n][5, k],{n,0,4}, {k, n, 5*n}]//Flatten