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A305197
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Number of set partitions of [n] with symmetric block size list of length A004525(n).
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4
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1, 1, 1, 1, 3, 7, 19, 56, 171, 470, 2066, 10299, 31346, 91925, 559987, 3939653, 11954993, 36298007, 282835456, 2571177913, 7785919355, 24158837489, 229359684137, 2557117944391, 7731656573016, 24350208829581, 272633076900991, 3601150175699409, 10876116332074739
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = A275281(n,(n+sin(n*Pi/2))/2).
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MAPLE
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b:= proc(n, s) option remember; expand(`if`(n>s,
binomial(n-1, n-s-1)*x, 1)+add(binomial(n-1, j-1)*
b(n-j, s+j)*binomial(s+j-1, j-1), j=1..(n-s)/2)*x^2)
end:
a:= n-> coeff(b(n, 0), x, (n+sin(n*Pi/2))/2):
seq(a(n), n=0..30);
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MATHEMATICA
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b[n_, s_] := b[n, s] = Expand[If[n > s, Binomial[n - 1, n - s - 1]*x, 1] + Sum[Binomial[n - 1, j - 1]*b[n - j, s + j]*Binomial[s + j - 1, j - 1], {j, 1, (n - s)/2}]*x^2];
a[n_] := Coefficient[b[n, 0], x, (n + Sin[n*Pi/2])/2];
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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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