A002867
a(n) = binomial(n,floor(n/2))*(n+1)!.
Original entry on oeis.org
1, 2, 12, 72, 720, 7200, 100800, 1411200, 25401600, 457228800, 10059033600, 221298739200, 5753767219200, 149597947699200, 4487938430976000, 134638152929280000, 4577697199595520000, 155641704786247680000, 5914384781877411840000, 224746621711341649920000
Offset: 0
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- T. D. Noe, Table of n, a(n) for n = 0..100
- Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
- Theodore S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
- OEIS Wiki, Sorting numbers.
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Table[Binomial[n,Floor[n/2]](n+1)!,{n,0,20}] (* Harvey P. Dale, Sep 04 2018 *)
A002871
a(n) = max_{k=0..n} 2^k*A048993(n,k).
Original entry on oeis.org
1, 2, 4, 12, 48, 200, 1040, 5600, 33600, 222432, 1460928, 11487168, 84713728, 731574272, 6314147840, 55456727040, 548291597568, 5226494727168, 54361802626560, 586042688924160, 6149776714099200, 72895623466265600, 855187250563024896
Offset: 0
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- Alois P. Heinz, Table of n, a(n) for n = 0..250
- Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
- T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
- OEIS Wiki, Sorting numbers
- Index entries for sequences related to sorting
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a:= n-> max(seq(2^k*Stirling2(n, k), k=0..n)):
seq(a(n), n=0..30); # Alois P. Heinz, Mar 26 2013
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a[n_] := Max[Table[2^k*StirlingS2[n, k], {k, 0, n}]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 25 2015 *)
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a(n) = vecmax(vector(n+1, k, 2^(k-1)*stirling(n, k-1, 2))); \\ Michel Marcus, Feb 25 2015
Original entry on oeis.org
1, 2, 5, 18, 91, 592, 4643, 42276, 436629, 5033182, 63974273, 888047414, 13358209647, 216334610860, 3751352135263, 69325155322184, 1359759373992105, 28206375825238458, 616839844140642301, 14181213537729200474, 341879141423814854915, 8623032181189674581256
Offset: 0
a(20) = 1 + 1 + 3 + 13 + 73 + 501 + 4051 + 37633 + 394353 + 4596553 + 58941091 + 824073141 + 12470162233 + 202976401213 + 3535017524403 + 65573803186921 + 1290434218669921 + 26846616451246353 + 588633468315403843 + 13564373693588558173 + 327697927886085654441.
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l:= func< n,b | Evaluate(LaguerrePolynomial(n), b) >;
[n eq 0 select 1 else 1 + (&+[ Factorial(j)*( l(j,-1) - l(j-1,-1) ): j in [1..n]]): n in [0..25]]; // G. C. Greubel, Mar 09 2021
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b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*j!*binomial(n-1, j-1), j=1..n))
end:
a:= proc(n) option remember; b(n)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..25); # Alois P. Heinz, May 11 2016
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With[{m = 25}, CoefficientList[Exp[x/(1-x)] + O[x]^m, x] Range[0, m-1]!// Accumulate] (* Jean-François Alcover, Nov 21 2020 *)
Table[1 +Sum[j!*(LaguerreL[j, -1] -LaguerreL[j-1, -1]), {j,n}], {n,0,30}] (* G. C. Greubel, Mar 09 2021 *)
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[1 + sum(factorial(j)*(gen_laguerre(j,0,-1) - gen_laguerre(j-1,0,-1)) for j in (1..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
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