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A168292
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T(n,k) = 24*A046802(n+1,k+1) - 9*A008518(n,k) - 8*A007318(n,k), triangle read by rows (0 <= k <= n).
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8
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7, 7, 7, 7, 38, 7, 7, 99, 99, 7, 7, 220, 546, 220, 7, 7, 461, 2236, 2236, 461, 7, 7, 942, 8001, 15596, 8001, 942, 7, 7, 1903, 26697, 89921, 89921, 26697, 1903, 7, 7, 3824, 85660, 463520, 796594, 463520, 85660, 3824, 7, 7, 7665, 268530, 2224350, 6068400
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..49.
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FORMULA
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E.g.f.: 24*(1 - x)*exp(t)/(1 - x*exp(t*(1 - x))) - 9*(exp(t) - x*exp(t*x))/(exp(t*x) - x*exp(t)) - 8*exp(t*(1 + x)).
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EXAMPLE
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Triangle begins:
7;
7, 7;
7, 38, 7;
7, 99, 99, 7;
7, 220, 546, 220, 7;
7, 461, 2236, 2236, 461, 7;
7, 942, 8001, 15596, 8001, 942, 7;
7, 1903, 26697, 89921, 89921, 26697, 1903, 7;
7, 3824, 85660, 463520, 796594, 463520, 85660, 3824, 7;
... reformatted. - Franck Maminirina Ramaharo, Oct 21 2018
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PROG
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(Maxima)
A123125(n, k) := sum((-1)^(k - j)*(binomial(n - j, k - j))*stirling2(n, j)*j!, j, 0, k)$
A046802(n, k) := sum(binomial(n - 1, r)*A123125(r, k - 1), r, k - 1, n - 1)$
A008518(n, k) := A123125(n, k) + A123125(n, k + 1)$
T(n, k) := 24*A046802(n + 1, k + 1) - 9*A008518(n, k) - 8*binomial(n, k)$
create_list(T(n, k), n, 0, 10, k, 0, n);
/* Franck Maminirina Ramaharo, Oct 21 2018 */
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CROSSREFS
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Triangles related to Eulerian numbers: A008292, A046802, A060187, A123125.
Cf. A142147, A142175, A168287, A168288, A168289, A168290, A168291, A168293.
Sequence in context: A337537 A003880 A084503 * A024733 A252732 A011472
Adjacent sequences: A168289 A168290 A168291 * A168293 A168294 A168295
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KEYWORD
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nonn,easy,less,tabl
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AUTHOR
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Roger L. Bagula, Nov 22 2009
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EXTENSIONS
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Edited, new name from Franck Maminirina Ramaharo, Oct 21 2018
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STATUS
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approved
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