A193972 - OEIS

A193972

Mirror of the triangle A193971.

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

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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:

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: A318578 A119435 A352783 * A361398 A332357 A305126

Adjacent sequences: A193969 A193970 A193971 * A193973 A193974 A193975

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved