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A193972 Mirror of the triangle A193971. 2
2, 5, 3, 9, 11, 4, 14, 26, 19, 5, 20, 50, 55, 29, 6, 27, 85, 125, 99, 41, 7, 35, 133, 245, 259, 161, 55, 8, 44, 196, 434, 574, 476, 244, 71, 9, 54, 276, 714, 1134, 1176, 804, 351, 89, 10, 65, 375, 1110, 2058, 2562, 2190, 1275, 485, 109, 11, 77, 495, 1650 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A193972 is obtained by reversing the rows of the triangle A193971.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

Write w(n,k) for the triangle at A193971.  The triangle at A193972 is then given by w(n,n-k).

EXAMPLE

First six rows:

2

5....3

9....11...4

14...26...19....5

20...50...55....29...6

27...85...125...99...41...7

MATHEMATICA

z = 11;

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

q[n_, x_] := (x + 1)^n

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}]]  (* A193971 *)

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

Flatten[Table[h[n], {n, -1, z}]]  (* A193972 *)

CROSSREFS

Cf. A193971.

Sequence in context: A319499 A318578 A119435 * A332357 A305126 A044043

Adjacent sequences:  A193969 A193970 A193971 * A193973 A193974 A193975

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified December 2 01:47 EST 2021. Contains 349435 sequences. (Running on oeis4.)