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| NAME
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allocatedTriangle of coefficients of polynomials u(n,x) jointly generated with A210756; see forthe ClarkFormula Kimberlingsection.
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| DATA
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1, 2, 3, 3, 11, 7, 4, 26, 38, 17, 5, 50, 124, 121, 41, 6, 85, 314, 499, 362, 99, 7, 133, 679, 1555, 1805, 1043, 239, 8, 196, 1316, 4054, 6672, 6096, 2926, 577, 9, 276, 2352, 9318, 20326, 26048, 19610, 8049, 1393, 10, 375, 3948, 19482, 53932, 90706
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| OFFSET
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1,2
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| COMMENTS
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Row n starts with n and ends with A001333(n).
Column 2: A051925
Row sums: A002450
Alternating row sums: 1,-1,-1,-1,-1,-1,...
For a discussion and guide to related arrays, see A208510.
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| FORMULA
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u(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+(x+1)*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...3
3...11...7
4...26...38....17
5...50...124...121...41
First three polynomials u(n,x): 1, 2 + 3x, 3 + 11x + 7x^2.
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| MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A210755 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210756 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)
Table[v[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)
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| CROSSREFS
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Cf. A210754, A208510.
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| KEYWORD
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allocated
nonn,tabl
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| AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Mar 25 2012
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| STATUS
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approved
editing
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