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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.

%I A216379 #10 Sep 02 2016 04:11:10
%S A216379 1,1,15,25,10,1,16,1280,9080,16944,12052,3840,580,40,1,1296,330480,
%T A216379 6148872,28245672,49658508,41392620,18428400,4691412,706833,63375,
%U A216379 3285,90,1,331776,207028224,8190885888,74684104704,253100173824,405044582400,351783415296,181005401088,58436640576,12288192000,1721191680,162115584,10228144,423360,10960,160,1
%N 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.
%e A216379 {1},
%e A216379 {1,15,25,10,1},
%e A216379 {16,1280,9080,16944,12052,3840,580,40,1}
%e A216379 ...
%t A216379 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
%Y A216379 Cf. A182924.
%Y A216379 Second row (n=1) is 5th row of A008277 (Stirling numbers S2).
%Y A216379 Third row is 5th row of A078739 (Generalized Stirling numbers S_{2,2}).
%Y A216379 Fourth row is 5th row of A078741 (Generalized Stirling numbers S_{3,3}).
%Y A216379 Fifth row is 5th row of A090214 (Generalized Stirling numbers S_{4,4}).
%K A216379 nonn,tabf,easy
%O A216379 0,3
%A A216379 _Jean-François Alcover_, Sep 06 2012