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A193964 Mirror of the triangle A193963. 2
1, 1, 4, 5, 20, 9, 14, 56, 45, 16, 30, 120, 126, 80, 25, 55, 220, 270, 224, 125, 36, 91, 364, 495, 480, 350, 180, 49, 140, 560, 819, 880, 750, 504, 245, 64, 204, 816, 1260, 1456, 1375, 1080, 686, 320, 81, 285, 1140, 1836, 2240, 2275, 1980, 1470, 896 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A193964 is obtained by reversing the rows of the triangle A193963.

LINKS

Table of n, a(n) for n=0..52.

FORMULA

Write w(n,k) for the triangle at A193963.  The triangle at A193964 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

1....4

5....20....9

14...56....45....16

30...120...126...80....25

55...220...270...224...125...36

MATHEMATICA

p[n_, x_] := Sum[((k + 1)^2)*x^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}]]  (* A193963 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193964 *)

CROSSREFS

Cf. A193963.

Sequence in context: A346060 A041255 A042835 * A337443 A099897 A050251

Adjacent sequences:  A193961 A193962 A193963 * A193965 A193966 A193967

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified November 28 16:42 EST 2021. Contains 349413 sequences. (Running on oeis4.)