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A340508
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Let ped(n) denote the number of partitions of n in which the even parts are distinct (A001935); a(n) = ped(9*n+7).
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1
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12, 132, 876, 4416, 18624, 69060, 232044, 720648, 2097612, 5781120, 15203904, 38387556, 93503052, 220586244, 505673280, 1129518564, 2464116480, 5260683840, 11010018840, 22623235620, 45700246668, 90863466372, 178000194348, 343888491684, 655760533632, 1235186054724
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OFFSET
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0,1
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COMMENTS
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These are the coefficients in the left-hand side of a "surprising identity" [Hirschhorn].
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REFERENCES
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M. D. Hirschhorn, The Power of q, Springer, 2017. See (33.1.3) page 303.
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LINKS
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FORMULA
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MAPLE
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with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
`if`(irem(d, 4)=0, 0, d), d=divisors(j)), j=1..n)/n)
end:
a:= n-> b(9*n+7):
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MATHEMATICA
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b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j]*Sum[
If[Mod[d, 4] == 0, 0, d], {d, Divisors[j]}], {j, 1, n}]/n];
a[n_] := b[9n+7];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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