cp's OEIS Frontend

A343936 Number of ways to choose a multiset of n divisors of n - 1.

%I A343936 #8 May 06 2021 21:24:33
%S A343936 1,2,3,10,5,56,7,120,45,220,11,4368,13,560,680,3876,17,26334,19,42504,
%T A343936 1771,2024,23,2035800,325,3276,3654,201376,29,8347680,31,376992,6545,
%U A343936 7140,7770,145008513,37,9880,10660,53524680,41,73629072,43,1712304,1906884
%N A343936 Number of ways to choose a multiset of n divisors of n - 1.
%F A343936 a(n) = ((sigma(n - 1), n)) = binomial(sigma(n - 1) + n - 1, n) where sigma = A000005 and binomial = A007318.
%e A343936 The a(1) = 1 through a(5) = 5 multisets:
%e A343936   {}  {1}  {1,1}  {1,1,1}  {1,1,1,1}
%e A343936       {2}  {1,3}  {1,1,2}  {1,1,1,5}
%e A343936            {3,3}  {1,1,4}  {1,1,5,5}
%e A343936                   {1,2,2}  {1,5,5,5}
%e A343936                   {1,2,4}  {5,5,5,5}
%e A343936                   {1,4,4}
%e A343936                   {2,2,2}
%e A343936                   {2,2,4}
%e A343936                   {2,4,4}
%e A343936                   {4,4,4}
%e A343936 The a(6) = 56 multisets:
%e A343936   11111  11136  11333  12236  13366  22266  23666
%e A343936   11112  11166  11336  12266  13666  22333  26666
%e A343936   11113  11222  11366  12333  16666  22336  33333
%e A343936   11116  11223  11666  12336  22222  22366  33336
%e A343936   11122  11226  12222  12366  22223  22666  33366
%e A343936   11123  11233  12223  12666  22226  23333  33666
%e A343936   11126  11236  12226  13333  22233  23336  36666
%e A343936   11133  11266  12233  13336  22236  23366  66666
%t A343936 multchoo[n_,k_]:=Binomial[n+k-1,k];
%t A343936 Table[multchoo[DivisorSigma[0,n],n-1],{n,50}]
%Y A343936 The version for chains of divisors is A163767.
%Y A343936 Diagonal n = k + 1 of A343658.
%Y A343936 Choosing n divisors of n gives A343935.
%Y A343936 A000005 counts divisors.
%Y A343936 A000312 = n^n.
%Y A343936 A007318 counts k-sets of elements of {1..n}.
%Y A343936 A009998 = n^k (as an array, offset 1).
%Y A343936 A059481 counts k-multisets of elements of {1..n}.
%Y A343936 A146291 counts divisors of n with k prime factors (with multiplicity).
%Y A343936 A253249 counts nonempty chains of divisors of n.
%Y A343936 Strict chains of divisors:
%Y A343936 - A067824 counts strict chains of divisors starting with n.
%Y A343936 - A074206 counts strict chains of divisors from n to 1.
%Y A343936 - A251683 counts strict length k + 1 chains of divisors from n to 1.
%Y A343936 - A334996 counts strict length-k chains of divisors from n to 1.
%Y A343936 - A337255 counts strict length-k chains of divisors starting with n.
%Y A343936 - A337256 counts strict chains of divisors of n.
%Y A343936 - A343662 counts strict length-k chains of divisors.
%Y A343936 Cf. A062319, A143773, A163767, A176029, A327527, A334997, A343656, A343661.
%K A343936 nonn
%O A343936 1,2
%A A343936 _Gus Wiseman_, May 05 2021