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A320823 Number of partitions of n with exactly ten sorts of part 1 which are introduced in ascending order.

%I A320823 #4 Oct 21 2018 12:52:23
%S A320823 1,55,1706,39381,754514,12703792,194550591,2771831836,37320172644,
%T A320823 480276118242,5957871478583,71707499618340,841619253647975,
%U A320823 9671546736478641,109173363429796284,1213748225365119080,13319241381691393856,144529657166520849546
%N A320823 Number of partitions of n with exactly ten sorts of part 1 which are introduced in ascending order.
%H A320823 Alois P. Heinz, <a href="/A320823/b320823.txt">Table of n, a(n) for n = 10..1006</a>
%F A320823 a(n) = A320741(n) - A320740(n).
%p A320823 b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
%p A320823       Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
%p A320823     end:
%p A320823 a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(10):
%p A320823 seq(a(n), n=10..35);
%Y A320823 Column k=10 of A292746.
%Y A320823 Cf. A320740, A320741.
%K A320823 nonn
%O A320823 10,2
%A A320823 _Alois P. Heinz_, Oct 21 2018