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A207622
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Triangle of coefficients of polynomials u(n,x) jointly generated with A207623; see the Formula section.
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3
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1, 2, 4, 2, 7, 8, 11, 22, 4, 16, 50, 24, 22, 100, 88, 8, 29, 182, 252, 64, 37, 308, 616, 296, 16, 46, 492, 1344, 1032, 160, 56, 750, 2688, 3000, 896, 32, 67, 1100, 5016, 7656, 3696, 384, 79, 1562, 8844, 17688, 12496, 2528, 64, 92, 2158, 14872, 37752
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OFFSET
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1,2
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COMMENTS
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With offset 0, equals the stretched Riordan array ((1 - z + z^2)/(1 - z)^3, 2*z^2/(1 - z)^2) in the notation of Corsani et al., Section 2. Cf. A207616. - Peter Bala, Dec 31 2015
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LINKS
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FORMULA
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u(n,x) = u(n-1,x) + v(n-1,x), v(n,x) = 2*x*u(n-1,x) + v(n-1,x) + 1, where u(1,x) = 1, v(1,x) = 1.
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EXAMPLE
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First five rows:
1
2
4 2
7 8
11 22 4
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := 2 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]
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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