A320819 - OEIS

%I #5 Oct 21 2018 12:29:13

%S 1,21,267,2668,23116,182443,1349703,9529538,64991613,431754668,

%T 2810794455,18011999644,113994583260,714334592349,4440885185275,

%U 27431944561645,168574045898166,1031553703902986,6290661582662655,38253841380267660,232085126723073278

%N Number of partitions of n with exactly six sorts of part 1 which are introduced in ascending order.

%H Alois P. Heinz, <a href="/A320819/b320819.txt">Table of n, a(n) for n = 6..1288</a>

%F a(n) = A320737(n) - A320736(n).

%p b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(

%p       Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))

%p     end:

%p a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(6):

%p seq(a(n), n=6..35);

%Y Column k=6 of A292746.

%Y Cf. A320736, A320737.

%K nonn

%O 6,2

%A _Alois P. Heinz_, Oct 21 2018