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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
OFFSET
0,1
COMMENTS
A193978 is obtained by reversing the rows of the triangle A193977.
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: A255737 A366741 A271371 * A224486 A163782 A362140
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved