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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 (list; table; graph; refs; listen; history; text; internal format)
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,n-k).

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

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Last modified December 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)