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A168287
T(n,k) = 2*A046802(n+1,k+1) - A007318(n,k), triangle read by rows (0 <= k <= n).
8
1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 60, 26, 1, 1, 57, 252, 252, 57, 1, 1, 120, 931, 1746, 931, 120, 1, 1, 247, 3201, 10187, 10187, 3201, 247, 1, 1, 502, 10534, 53542, 89788, 53542, 10534, 502, 1, 1, 1013, 33698, 262466, 688976, 688976, 262466, 33698, 1013
OFFSET
0,5
FORMULA
E.g.f.: 2*(1 - x)*exp(t)/(1 - x*exp(t*(1 - x))) - exp(t*(1 + x)).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 4, 1;
1, 11, 11, 1;
1, 26, 60, 26, 1;
1, 57, 252, 252, 57, 1;
1, 120, 931, 1746, 931, 120, 1;
1, 247, 3201, 10187, 10187, 3201, 247, 1;
1, 502, 10534, 53542, 89788, 53542, 10534, 502, 1;
... reformatted. - Franck Maminirina Ramaharo, Oct 21 2018
MATHEMATICA
p[t_] = 2*(1 - x)*Exp[t]/(1 - x*Exp[t*(1 - x)]) - Exp[t*(1 + x)];
Table[CoefficientList[FullSimplify[n!*SeriesCoefficient[Series[p[t], {t, 0, n}], n]], x], {n, 0, 10}]//Flatten
PROG
(Maxima)
A046802(n, k) := sum(binomial(n - 1, r)*sum(j!*(-1)^(k - j - 1)*stirling2(r, j)*binomial(r - j, k - j - 1), j, 0, k - 1), r, k - 1, n - 1)$
T(n, k) := 2*A046802(n + 1, k + 1) - binomial(n, k)$
create_list(T(n, k), n, 0, 10, k, 0, n);
/* Franck Maminirina Ramaharo, Oct 21 2018 */
CROSSREFS
Triangles related to Eulerian numbers: A008292, A046802, A060187, A123125.
Sequence in context: A324916 A156534 A375858 * A221987 A285357 A174526
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Nov 22 2009
EXTENSIONS
Edited, and new name by Franck Maminirina Ramaharo, Oct 21 2018
STATUS
approved