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A193974 Mirror of the triangle A193973. 4
2, 5, 3, 9, 7, 4, 14, 12, 9, 5, 20, 18, 15, 11, 6, 27, 25, 22, 18, 13, 7, 35, 33, 30, 26, 21, 15, 8, 44, 42, 39, 35, 30, 24, 17, 9, 54, 52, 49, 45, 40, 34, 27, 19, 10, 65, 63, 60, 56, 51, 45, 38, 30, 21, 11, 77, 75, 72, 68, 63, 57, 50, 42, 33, 23, 12, 90, 88, 85, 81 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A193974 is obtained by reversing the rows of the triangle A193973.

LINKS

Table of n, a(n) for n=0..69.

FORMULA

Write w(n,k) for the triangle at A193973.  The triangle at A193974 is then given by w(n,n-k).

EXAMPLE

First six rows:

2

5....3

9....7....4

14...12...9....5

20...18...15...11...6

27...25...22...18...13...7

MATHEMATICA

z = 13;

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

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}]]  (* A193973 *)

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

Flatten[Table[h[n], {n, -1, z}]]  (* A193974 *)

CROSSREFS

Cf. A193973.

Sequence in context: A122281 A340927 A182480 * A319499 A318578 A119435

Adjacent sequences:  A193971 A193972 A193973 * A193975 A193976 A193977

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified November 28 00:12 EST 2021. Contains 349395 sequences. (Running on oeis4.)