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A225474
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Triangle read by rows, k!*2^k*s_2(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0.
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0
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1, 1, 2, 3, 8, 8, 15, 46, 72, 48, 105, 352, 688, 768, 384, 945, 3378, 7600, 11040, 9600, 3840, 10395, 39048, 97112, 167040, 193920, 138240, 46080, 135135, 528414, 1418648, 2754192, 3857280, 3736320, 2257920, 645120, 2027025, 8196480, 23393376, 49824768, 79892736
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OFFSET
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0,3
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COMMENTS
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The Stirling-Frobenius cycle numbers are defined in A225470.
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LINKS
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FORMULA
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For a recurrence see the Sage program.
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EXAMPLE
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[n\k][ 0, 1, 2, 3, 4, 5]
[0] 1,
[1] 1, 2,
[2] 3, 8, 8,
[3] 15, 46, 72, 48,
[4] 105, 352, 688, 768, 384,
[5] 945, 3378, 7600, 11040, 9600, 3840.
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MATHEMATICA
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SFCSO[n_, k_, m_] := SFCSO[n, k, m] = If[k>n || k<0, 0, If[n == 0 && k == 0, 1, m*k*SFCSO[n-1, k-1, m] + (m*n-1)*SFCSO[n-1, k, m]]]; Table[SFCSO[n, k, 2], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 05 2014, translated from Sage *)
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PROG
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(Sage)
@CachedFunction
def SF_CSO(n, k, m):
if k > n or k < 0 : return 0
if n == 0 and k == 0: return 1
return m*k*SF_CSO(n-1, k-1, m) + (m*n-1)*SF_CSO(n-1, k, m)
for n in (0..8): [SF_CSO(n, k, 2) for k in (0..n)]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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