

A193962


Mirror of the triangle A193961.


2



1, 4, 1, 40, 17, 4, 184, 98, 40, 9, 584, 354, 184, 73, 16, 1484, 979, 584, 298, 116, 25, 3248, 2275, 1484, 874, 440, 169, 36, 6384, 4676, 3248, 2099, 1224, 610, 232, 49, 11568, 8772, 6384, 4403, 2824, 1634, 808, 305, 64, 19668, 15333, 11568, 8372
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OFFSET

0,2


COMMENTS

A193962 is obtained by reversing the rows of the triangle A193961.


LINKS

Table of n, a(n) for n=0..48.


FORMULA

Write w(n,k) for the triangle at A193961. The triangle at A193962 is then given by w(n,nk).


EXAMPLE

First six rows:
1
4......1
40.....17....4
184....98....40....9
584....354...184...73...16
1484...979...584...298..116..25


MATHEMATICA

z = 12;
p[n_, x_] := Sum[((k + 1)^2)*x^(n  k), {k, 0, n}]
q[n_, x_] := p[n, x]
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x > 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1  k, x], {k, 0, n}]; w[1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, 1, z}]]
Flatten[Table[Reverse[g[n]], {n, 1, z}]] (* A193961 *)
TableForm[Table[g[n], {n, 1, z}]]
Flatten[Table[g[n], {n, 1, z}]] (* A193962 *)


CROSSREFS

Cf. A193961.
Sequence in context: A303987 A297900 A298495 * A302441 A269906 A092667
Adjacent sequences: A193959 A193960 A193961 * A193963 A193964 A193965


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 10 2011


STATUS

approved



