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A193978
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Mirror of the triangle A193977.
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2
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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A193978 is obtained by reversing the rows of the triangle A193977.
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LINKS
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Table of n, a(n) for n=0..58.
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FORMULA
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Write w(n,k) for the triangle at A193977. The triangle at A193978 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
2
5....6
9....14...12
14...24...27...20
20...36...45...44...30
27...50...66...72...65...42
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A193977.
Sequence in context: A190678 A255737 A271371 * A224486 A163782 A226793
Adjacent sequences: A193975 A193976 A193977 * A193979 A193980 A193981
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Aug 10 2011
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STATUS
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approved
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