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September Morn Update

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Ingy döt Net 2019-09-12 10:33:56 -07:00
parent 4e2d22a71d
commit aac6731f2c
6856 changed files with 141342 additions and 21127 deletions
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16
Task/Paraffins/Mathematica/paraffins.math
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@ -1,14 +1,10 @@
s[m_, p_, n_] :=
CycleIndexPolynomial[SymmetricGroup[m],
Table[ComposeSeries[p, x^i + O[x]^(n + 1)], {i, m}]];
G000598[n_] := Nest[1 + x s[3, #, n] &, 1 + O[x], n];
G000602[n_] :=
Block[{x},
x*CycleIndexPolynomial[SymmetricGroup[4],
Table[ComposeSeries[#, x^i + O[x]^(n + 1)], {i, 4}]] -
CycleIndexPolynomial[SymmetricGroup[2],
Table[ComposeSeries[# - 1, x^i + O[x]^(n + 1)], {i, 2}]] +
ComposeSeries[#, x^2 + O[x]^(n + 1)] &@
Fold[Series[
1 + x/6 (#1^3 + 3 #1 ComposeSeries[#1, x^2 + O[x]^#2] +
2 ComposeSeries[#1, x^3 + O[x]^#2]), {x, 0, #2}] &,
1 + O[x], Range[n + 1]]];
x s[4, #, n] - s[2, # - 1, n] +
ComposeSeries[#, x^2 + O[x]^(n + 1)] &[G000598[n]];
A000602[n_] := SeriesCoefficient[G000602[n], n];
A000602List[n_] := CoefficientList[G000602[n], x];
Grid@Transpose@{Range[0, 200], A000602List@200}