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A207616
Triangle of coefficients of polynomials u(n,x) jointly generated with A207617; see the Formula section.
4
1, 2, 4, 1, 7, 4, 11, 11, 1, 16, 25, 6, 22, 50, 22, 1, 29, 91, 63, 8, 37, 154, 154, 37, 1, 46, 246, 336, 129, 10, 56, 375, 672, 375, 56, 1, 67, 550, 1254, 957, 231, 12, 79, 781, 2211, 2211, 781, 79, 1, 92, 1079, 3718, 4719, 2288, 377, 14, 106, 1456, 6006
OFFSET
1,2
COMMENTS
With offset 0, equals the stretched Riordan array ((1 - z + z^2)/(1 - z)^3, z^2/(1 - z)^2) in the notation of Corsani et al., Section 2. - Peter Bala, Dec 31 2015
LINKS
C. Corsani, D. Merlini, and R. Sprugnoli, Left-inversion of combinatorial sums, Discrete Mathematics, 180 (1998) 107-122.
FORMULA
u(n,x) = u(n-1,x) + v(n-1,x), v(n,x) = x*u(n-1,x) + v(n-1,x) + 1, where u(1,x) = 1, v(1,x) = 1.
EXAMPLE
First five rows:
1
2
4 1
7 4
11 11 1
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A207616 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207617 *)
CROSSREFS
Cf. A207617, A208510, A000124 (column 1).
Sequence in context: A374116 A256107 A207610 * A105552 A112852 A121531
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved