A320823 - OEIS

%I #4 Oct 21 2018 12:52:23

%S 1,55,1706,39381,754514,12703792,194550591,2771831836,37320172644,

%T 480276118242,5957871478583,71707499618340,841619253647975,

%U 9671546736478641,109173363429796284,1213748225365119080,13319241381691393856,144529657166520849546

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

%H Alois P. Heinz, <a href="/A320823/b320823.txt">Table of n, a(n) for n = 10..1006</a>

%F a(n) = A320741(n) - A320740(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))(10):

%p seq(a(n), n=10..35);

%Y Column k=10 of A292746.

%Y Cf. A320740, A320741.

%K nonn

%O 10,2

%A _Alois P. Heinz_, Oct 21 2018