A168290 T(n,k) = 5*A046802(n+1,k+1) - 4*A007318(n,k), triangle read by rows (0 <= k <= n).

1, 1, 1, 1, 7, 1, 1, 23, 23, 1, 1, 59, 141, 59, 1, 1, 135, 615, 615, 135, 1, 1, 291, 2305, 4335, 2305, 291, 1, 1, 607, 7971, 25415, 25415, 7971, 607, 1, 1, 1243, 26293, 133771, 224365, 133771, 26293, 1243, 1, 1, 2519, 84191, 656039, 1722251, 1722251, 656039

Offset

0,5

Links

Table of n, a(n) for n=0..51.

Formula

E.g.f.: 5*(1 - x)*exp(t)/(1 - x*exp(t*(1 - x))) - 4*exp(t*(1 + x)).

Example

Triangle begins:
    1;
    1,    1;
    1,    7,     1;
    1,   23,    23,      1;
    1,   59,   141,     59,      1;
    1,  135,   615,    615,    135,      1;
    1,  291,  2305,   4335,   2305,    291,     1;
    1,  607,  7971,  25415,  25415,   7971,   607,    1;
    1, 1243, 26293, 133771, 224365, 133771, 26293, 1243, 1;
     ... reformatted. - Franck Maminirina Ramaharo, Oct 21 2018

Mathematica

p[t_] = 5*(1 - x)*Exp[t]/(1 - x*Exp[t*(1 - x)]) - 4*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) := 5*A046802(n + 1, k + 1) - 4*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.

Cf. A142147, A142175, A168287, A168288, A168289, A168291, A168292, A168293.

Sequence in context: A046739 A056752 A053714 * A218695 A179837 A238743

Adjacent sequences: A168287 A168288 A168289 * A168291 A168292 A168293

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Nov 22 2009

Extensions

Edited, new name by Franck Maminirina Ramaharo, Oct 21 2018

Status

approved