cp's OEIS Frontend

A343661 Sum of numbers of y-multisets of divisors of x for each x >= 1, y >= 0, x + y = n.

%I A343661 #6 Apr 30 2021 17:16:05
%S A343661 1,2,4,7,12,19,30,46,70,105,155,223,316,443,619,865,1210,1690,2354,
%T A343661 3263,4497,6157,8368,11280,15078,19989,26296,34356,44626,57693,74321,
%U A343661 95503,122535,157101,201377,258155,330994,424398,544035,696995,892104,1140298,1455080
%N A343661 Sum of numbers of y-multisets of divisors of x for each x >= 1, y >= 0, x + y = n.
%F A343661 a(n) = Sum_{k=1..n} binomial(sigma(k) + n - k - 1, n - k).
%e A343661 The a(5) = 12 multisets of divisors:
%e A343661   {1,1,1,1}  {1,1,1}  {1,1}  {1}  {}
%e A343661              {1,1,2}  {1,3}  {2}
%e A343661              {1,2,2}  {3,3}  {4}
%e A343661              {2,2,2}
%t A343661 multchoo[n_,k_]:=Binomial[n+k-1,k];
%t A343661 Table[Sum[multchoo[DivisorSigma[0,k],n-k],{k,n}],{n,10}]
%Y A343661 Antidiagonal sums of the array A343658 (or row sums of the triangle).
%Y A343661 Dominates A343657.
%Y A343661 A000005 counts divisors.
%Y A343661 A007318 counts k-sets of elements of {1..n}.
%Y A343661 A059481 counts k-multisets of elements of {1..n}.
%Y A343661 A343656 counts divisors of powers.
%Y A343661 Cf. A000169, A000312, A009998, A062319, A067824, A143773, A146291, A176029, A184389, A285572, A326077, A327527, A334996, A343652, A343657.
%K A343661 nonn
%O A343661 1,2
%A A343661 _Gus Wiseman_, Apr 30 2021