A075186
Sixth column of triangle A075181 divided by 4!.
Original entry on oeis.org
5, 147, 3283, 67284, 1346625, 27061650, 553887180, 11636745120, 252045153360, 5641615980000, 130658463936000, 3132519418828800, 77747158404115200, 1997070421868121600, 53066619106300800000
Offset: 0
A075187
Seventh column of triangle A075181 divided by 4!.
Original entry on oeis.org
30, 1089, 29531, 723680, 17084650, 400186050, 9447948510, 226861274640, 5570383618800, 140328075888000, 3634144257744000, 96862561213017600, 2658662147043302400, 75165608074100544000, 2188816503237524160000
Offset: 0
A308941
a(n) = Product_{k=1..n} |Stirling1(n,k)| * k!.
Original entry on oeis.org
1, 1, 2, 72, 114048, 14515200000, 234709539840000000, 698712561855933972480000000, 523145284340194421434020324704256000000, 128974285815375032145715297526239008267285037056000000, 13271794881195622862513637643190449698396346431150489600000000000000000
Offset: 0
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Table[Product[Abs[StirlingS1[n, k]] k!, {k, 1, n}], {n, 0, 10}]
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a(n) = prod(k=1, n, abs(stirling(n, k, 1))*k!); \\ Michel Marcus, Jul 02 2019
A322342
Expansion of e.g.f. 1/(1 - log(1 + x)/(1 - log(1 + x)^2/(1 - log(1 + x)^3/(1 - ...)))), a continued fraction.
Original entry on oeis.org
1, 1, 1, 8, 16, 224, 1328, 8280, 192960, 337992, 33969672, 11690832, 7909754400, -2553028752, 2357881048560, 3942533549568, 661635400722048, 13397372969553792, -107825500036658304, 22964754191590789632, -572404186520543904768, 31472786179436211417600, -886973046496642227294720
Offset: 0
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nmax = 22; CoefficientList[Series[1/(1 + ContinuedFractionK[-Log[1 + x]^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
A225474
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.
Original entry on oeis.org
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
Offset: 0
[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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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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@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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