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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
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: A363677 A340927 A182480 * A319499 A318578 A119435
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)