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| NAME
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allocatedTriangle of coefficients of polynomials v(n,x) jointly generated with A209583; see forthe ClarkFormula Kimberlingsection.
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| DATA
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1, 3, 2, 5, 7, 3, 9, 18, 14, 4, 15, 42, 48, 25, 5, 25, 89, 137, 107, 41, 6, 41, 180, 348, 364, 212, 63, 7, 67, 350, 820, 1078, 844, 386, 92, 8, 109, 663, 1827, 2902, 2864, 1773, 659, 129, 9, 177, 1230, 3906, 7284, 8692, 6809, 3453, 1069, 175, 10, 287
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| OFFSET
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1,2
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| COMMENTS
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Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
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| FORMULA
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u(n,x)=x*u(n-1,x)+v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+(x+1)
where u(1,x)=1, v(1,x)=1.
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| EXAMPLE
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First five rows:
1
3....1
5....7....3
9....18...14...4
15...42...48...25...5
First three polynomials v(n,x): 1, 3 + x , 5 + 7x + 3x^2.
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| MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
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[%] (* A209583 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209584 *)
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| CROSSREFS
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Cf. A209583, 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 11 2012
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| STATUS
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approved
editing
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