

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
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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,nk).


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



