The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A226313 Number of commuting 4-tuples of elements from S_n, divided by n!. 3
 1, 8, 21, 84, 206, 717, 1810, 5462, 13859, 38497, 96113, 253206, 620480, 1566292, 3770933, 9212041, 21768608, 51795427, 120279052, 279849177, 639379257, 1459282932, 3283758256, 7369471795, 16351101855, 36147590987, 79162129897, 172646751524, 373527250619, 804631686843, 1721283389932, 3666041417241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Euler transform of A001001. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..9000 Tad White, Counting Free Abelian Actions, arXiv preprint arXiv:1304.2830, 2013 FORMULA a(n) ~ exp(2^(7/4) * Pi^(3/2) * Zeta(3)^(1/4) * n^(3/4) / (3^(3/2) * 5^(1/4)) - sqrt(5*Zeta(3)*n) / (2^(3/2)*Pi) + (sqrt(Pi) * 5^(1/4) / (2^(15/4) * 3^(3/2) * Zeta(3)^(1/4)) - sqrt(3) * 5^(5/4) * Zeta(3)^(3/4) / (2^(15/4) * Pi^(7/2))) * n^(1/4) - 25*Zeta(3) / (16*Pi^6) + (5 - 2*Zeta(3)) / (192*Pi^2)) * Pi^(1/4) * Zeta(3)^(1/8) / (2^(13/8) * 3^(1/4) * 5^(1/8) * n^(5/8)). - Vaclav Kotesovec, Mar 26 2018 MAPLE with(numtheory): b:= proc(n) option remember; add(d*sigma(d), d=divisors(n)) end: a:= proc(n) option remember; `if`(n=0, 1, add(add(d* b(d), d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=1..40); # Alois P. Heinz, Mar 06 2015 MATHEMATICA b[n_] := b[n] = DivisorSum[n, #*DivisorSigma[1, #]&]; a[n_] := a[n] = If[n == 0, 1, Sum[DivisorSum[j, #*b[#]&]*a[n-j], {j, 1, n}] /n]; Array[a, 40] (* Jean-François Alcover, Mar 27 2017, after Alois P. Heinz *) nmax = 40; Rest[CoefficientList[Series[Exp[Sum[Sum[Sum[d*DivisorSigma[1, d], {d, Divisors[k]}] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Mar 31 2018 *) CROSSREFS Cf. A001001, A061256, A301777. Sequence in context: A156304 A232049 A225658 * A275185 A264238 A188700 Adjacent sequences: A226310 A226311 A226312 * A226314 A226315 A226316 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 08 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 25 17:06 EDT 2023. Contains 361528 sequences. (Running on oeis4.)