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A193978 Mirror of the triangle A193977. 2
2, 5, 6, 9, 14, 12, 14, 24, 27, 20, 20, 36, 45, 44, 30, 27, 50, 66, 72, 65, 42, 35, 66, 90, 104, 105, 90, 56, 44, 84, 117, 140, 150, 144, 119, 72, 54, 104, 147, 180, 200, 204, 189, 152, 90, 65, 126, 180, 224, 255, 270, 266, 240, 189, 110, 77, 150, 216, 272 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A193978 is obtained by reversing the rows of the triangle A193977.

LINKS

Table of n, a(n) for n=0..58.

FORMULA

Write w(n,k) for the triangle at A193977.  The triangle at A193978 is then given by w(n,n-k).

EXAMPLE

First six rows:

2

5....6

9....14...12

14...24...27...20

20...36...45...44...30

27...50...66...72...65...42

MATHEMATICA

z = 11;

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

q[n_, x_] := Sum[(k + 1)*x^k, {k, 0, 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}]]  (* A193977 *)

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

Flatten[Table[h[n], {n, -1, z}]]  (* A193978 *)

CROSSREFS

Cf. A193977.

Sequence in context: A190678 A255737 A271371 * A224486 A163782 A226793

Adjacent sequences:  A193975 A193976 A193977 * A193979 A193980 A193981

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified March 8 00:38 EST 2021. Contains 341934 sequences. (Running on oeis4.)