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A207635
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Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section.
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3
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1, 2, 5, 2, 11, 9, 2, 23, 29, 13, 2, 47, 81, 55, 17, 2, 95, 209, 191, 89, 21, 2, 191, 513, 591, 369, 131, 25, 2, 383, 1217, 1695, 1329, 631, 181, 29, 2, 767, 2817, 4607, 4353, 2591, 993, 239, 33, 2, 1535, 6401, 12031, 13313, 9535, 4577, 1471, 305, 37, 2
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OFFSET
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1,2
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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)=(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
5....2
11...9....2
23...29...13...2
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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_] := (x + 1)*u[n - 1, x]
+ (x + 1)*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
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AUTHOR
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STATUS
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approved
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