A294373
Product of first n Bell numbers.
Original entry on oeis.org
1, 1, 2, 10, 150, 7800, 1583400, 1388641800, 5748977052000, 121573617718644000, 14099500314919737900000, 9567497928695086546803000000, 40313580569855830588349480391000000, 1114446238307803607782300144651734867000000
Offset: 0
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B:= map(combinat:-bell, [$0..19]):
map(i -> convert(B[1..i],`*`),[$1..20]); # Robert Israel, Oct 29 2017
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Table[Product[BellB[k], {k, 0, n}], {n, 0, 15}]
A058807
a(n) = Product_{k=1..n} s(n,k), where s(n,k) is unsigned Stirling number of the first kind. (s(n,k) = number of permutations of n elements which contain exactly k cycles.)
Original entry on oeis.org
1, 1, 6, 396, 420000, 9432450000, 5571367220160000, 103458225408290423193600, 70288262635020872178876253470720, 1993179010286886206697449779415040000000000, 2650683735711909138223088071500675703191552000000000000
Offset: 1
a(4) = s(4,1)*s(4,2)*s(4,3)*s(4,4) = 6*11*6*1 = 396.
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a:=n->mul(abs(Stirling1(n, k)), k=1..n): seq(a(n), n=1..10); # Zerinvary Lajos, Jun 28 2007
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Abs[Table[Product[StirlingS1[n,k],{k,n}],{n,10}]] (* Harvey P. Dale, Oct 18 2014 *)
A308942
a(n) = Product_{k=1..n} Stirling2(n,k) * k!.
Original entry on oeis.org
1, 1, 2, 36, 12096, 129600000, 67688524800000, 2447142088237056000000, 8252231792724705005273088000000, 3364251896526130462332506439942144000000000, 208568259979639958038116614964866564751360000000000000000, 2415411835199739880770061590576804904109473876860500705280000000000000000
Offset: 0
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Table[Product[StirlingS2[n, k] k!, {k, 1, n}], {n, 0, 11}]
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a(n) = prod(k=1, n, stirling(n, k, 2)*k!); \\ Michel Marcus, Jul 02 2019
A309171
a(n) = Product_{d|n} Stirling2(n,d).
Original entry on oeis.org
1, 1, 1, 7, 1, 2790, 1, 216027, 3025, 21730275, 1, 143362465643243568744, 1, 404056132480, 500592722458920, 12056706465173227408551, 1, 99260615209905051640711424376160950, 1, 105138504356810366747790360523498652392500, 143413971571112402506500, 768149712982621155186
Offset: 1
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[(&*[StirlingSecond(n,d): d in Divisors(n)]): n in [1..30]]; // Vincenzo Librandi, Jul 16 2019
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Table[Product[StirlingS2[n, d], {d, Divisors[n]}], {n, 1, 22}]
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a(n) = my(d=divisors(n)); prod(k=1, #d, stirling(n, d[k], 2)); \\ Michel Marcus, Jul 16 2019
Showing 1-4 of 4 results.