A372632 - OEIS

%I #16 May 10 2024 08:49:56

%S 0,1,2,4,6,9,16,21,33,47,67,90,134,172,242,321,434,558,761,961,1279,

%T 1627,2112,2657,3452,4292,5481,6824,8619,10634,13381,16389,20425,

%U 24989,30864,37556,46221,55912,68337,82510,100262,120476,145855,174562,210272,251065

%N Sum over all partitions of n of the number of elements with minimal multiplicity in their partition.

%H Alois P. Heinz, <a href="/A372632/b372632.txt">Table of n, a(n) for n = 0..2000</a>

%F a(n) = Sum_{k=0..A003056(n)} k * A362615(n,k).

%p b:= proc(n, i, m, t) option remember; `if`(n=0, t,

%p       `if`(i<1, 0, b(n, i-1, m, t)+add(b(n-i*j, i-1, min(j, m),

%p       `if`(j<m, 1, `if`(j=m, t+1, t))), j=1..n/i)))

%p     end:

%p a:= n-> b(n$3, 0):

%p seq(a(n), n=0..45);

%t b[n_, i_, m_, t_] := b[n, i, m, t] = If[n == 0, t,

%t    If[i < 1, 0, b[n, i - 1, m, t] + Sum[b[n - i*j, i - 1, Min[j, m],

%t    If[j < m, 1, If[j == m, t + 1, t]]], {j, 1, n/i}]]];

%t a[n_] := b[n, n, n, 0];

%t Table[a[n], {n, 0, 45}] (* _Jean-François Alcover_, May 10 2024, after _Alois P. Heinz_ *)

%Y Cf. A000041, A003056, A362615, A372542.

%K nonn

%O 0,3

%A _Alois P. Heinz_, May 07 2024