|
%I #17 Dec 16 2023 22:11:34
%S 1,1,1,2,4,10,29,101,367,1562,6891,37871,197930,1121634,6888085,
%T 46190282,323250987,2349020516,17897285514,142512956148,1178963284732,
%U 10248806222398,91421283039658,847666112839362,8100455404172267,79925567946537362,814508927747776069
%N Number of partitions of [n] whose block minima sum to k, where k is chosen so as to maximize this number.
%H Alois P. Heinz, <a href="/A365903/b365903.txt">Table of n, a(n) for n = 0..100</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p b:= proc(n, i, t, m) option remember; `if`(n=0, t^(m-i+1),
%p `if`((i+m)*(m+1-i)/2<n or i>n, 0, `if`(t=0, 0,
%p t*b(n, i+1, t, m))+ b(n-i, i+1, t+1, m)))
%p end:
%p a:= n-> max(seq(b(k, 1, 0, n), k=0..n*(n+1)/2)):
%p seq(a(n), n=0..26);
%p # second Maple program:
%p a:= proc(h) option remember; local b; b:=
%p proc(n, m) option remember; `if`(n=0, 1,
%p b(n-1, m)*m + expand(x^(h-n+1)*b(n-1, m+1)))
%p end: forget(b); max(coeffs(b(h, 0)))
%p end:
%p seq(a(n), n=0..26);
%Y Row maxima of A124327.
%Y Cf. A367969.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Dec 14 2023
|
