A308037
a(n) = Sum_{d|n} Stirling2(n,d).
Original entry on oeis.org
1, 2, 2, 9, 2, 123, 2, 1830, 3027, 43038, 2, 2023728, 2, 49337473, 213142023, 2313595723, 2, 216927216877, 2, 6712023695345, 82312699558575, 366282502967439, 2, 113350450913387211, 2436684974110753, 1850568574287104493, 106563274551407600878, 231678790379913209098, 2
Offset: 1
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a:= n-> add(Stirling2(n, d), d=numtheory[divisors](n)):
seq(a(n), n=1..30); # Alois P. Heinz, May 10 2019
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a[n_] := a[n] = Sum[StirlingS2[n, d], {d, Divisors[n]}]; Table[a[n], {n, 1, 29}]
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a(n) = sumdiv(n, d, stirling(n, d, 2)); \\ Michel Marcus, May 10 2019
A309169
a(n) = Product_{d|n} |Stirling1(n,d)|.
Original entry on oeis.org
1, 1, 2, 66, 24, 7398000, 720, 445824751680, 4762759680, 100329999065856000, 3628800, 1019618790465528595884298768746577920000, 479001600, 97532934291415606872784896000, 5460491900297503751785620701184000, 1567611138605648558776157123803950409816473600000
Offset: 1
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f:= proc(n) local d; mul(abs(combinat:-stirling1(n,d)),d=numtheory:-divisors(n)) end proc:
map(f, [$1..30]); # Robert Israel, Jul 15 2019
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Table[Product[Abs[StirlingS1[n, d]], {d, Divisors[n]}], {n, 1, 16}]
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a(n) = my(d=divisors(n)); prod(k=1, #d, abs(stirling(n, d[k], 1))); \\ Michel Marcus, Jul 16 2019
A309910
a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * floor(n/k).
Original entry on oeis.org
1, 3, 10, 53, 266, 2093, 14512, 134705, 1317724, 14339429, 156052942, 2243410945, 28893239818, 421448538895, 6810085942104, 117497037128065, 1980909279322608, 38790292385240321, 730946685781179418, 15916872348230275385, 346942995035062132634, 7767365425379382284307
Offset: 1
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Table[Sum[(-1)^(n - k) StirlingS1[n, k] Floor[n/k] , {k, 1, n}], {n, 1, 22}]
Table[SeriesCoefficient[1/(1 - x) Sum[(-1)^(n - k) StirlingS1[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 22}]
Table[Sum[Sum[(-1)^(n - d) StirlingS1[n, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 22}]
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a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1) * (n\k)); \\ Michel Marcus, Aug 23 2019
Showing 1-3 of 3 results.