

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
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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,nk).


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



