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

0,3

Links

Table of n, a(n) for n=0..44.

Example

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

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

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}).

Sequence in context: A167709 A167353 A219880 * A120746 A106613 A192542

Adjacent sequences: A216376 A216377 A216378 * A216380 A216381 A216382

Keyword

nonn,tabf,easy

Author

Jean-François Alcover, Sep 06 2012

Status

approved