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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Sep 06 2012

STATUS

approved

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Last modified June 26 04:09 EDT 2019. Contains 324369 sequences. (Running on oeis4.)