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A193950
Mirror of the triangle A193949.
2
1, 4, 2, 13, 8, 3, 45, 32, 19, 8, 120, 92, 64, 38, 15, 300, 242, 184, 128, 75, 30, 692, 578, 464, 352, 243, 142, 56, 1524, 1306, 1088, 872, 659, 454, 264, 104, 3225, 2818, 2411, 2006, 1604, 1210, 831, 482, 189, 6625, 5878, 5131, 4386, 3644, 2910, 2191
OFFSET
0,2
COMMENTS
A193950 is obtained by reversing the rows of the triangle A193949.
FORMULA
Write w(n,k) for the triangle at A193949. The triangle at A193950 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
4.....2
13....8.....3
45....32....19....8
120...92....64....38....15
300...242...184...128...75...30
MATHEMATICA
z = 12;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - k), {k, 0, n}];
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193949 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193950 *)
CROSSREFS
Cf. A193949.
Sequence in context: A224820 A125153 A191451 * A180194 A193853 A213853
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved