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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
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
KEYWORD
nonn,tabf,easy
AUTHOR
STATUS
approved

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Last modified March 1 12:27 EST 2024. Contains 370433 sequences. (Running on oeis4.)