A193861 - OEIS

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A193861

Mirror of the triangle A193860.

1, 5, 1, 19, 7, 1, 65, 33, 9, 1, 211, 131, 51, 11, 1, 665, 473, 233, 73, 13, 1, 2059, 1611, 939, 379, 99, 15, 1, 6305, 5281, 3489, 1697, 577, 129, 17, 1, 19171, 16867, 12259, 6883, 2851, 835, 163, 19, 1, 58025, 52905, 41385, 26025, 12585, 4521, 1161

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

A193861 is obtained by reversing the rows of the triangle A193860.

LINKS

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

FORMULA

Write w(n,k) for the triangle at A193860. The triangle at A193861 is then given by w(n,n-k).

EXAMPLE

First six rows:

5.....1

19....7.....1

65....33....9.....1

211...131...51....11...1

665...473...233...73...13...1

MATHEMATICA

z = 10;

p[n_, x_] := (2 x + 1)^n;

q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1;

p1[n_, k_] := Coefficient[p[n, x], x^k];

p1[n_, 0] := p[n, x] /. x -> 0;

d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

h[n_] := CoefficientList[d[n, x], {x}]

TableForm[Table[Reverse[h[n]], {n, 0, z}]]

Flatten[Table[Reverse[h[n]], {n, -1, z}]] (* A193860 *)

TableForm[Table[h[n], {n, 0, z}]]

Flatten[Table[h[n], {n, -1, z}]] (* A193861 *)

CROSSREFS

Cf. A193860.

Sequence in context: A297174 A226605 A055584 * A349544 A193857 A146055

Adjacent sequences: A193858 A193859 A193860 * A193862 A193863 A193864

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 07 2011

STATUS

approved