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A272522 Number of set partitions of [n] into ten blocks with distinct sizes.

%I A272522 #4 May 01 2016 20:06:32
%S A272522 1906765806522767212441719098019963758016000000,
%T A272522 9707171378661360354248751771737997313536000000,
%U A272522 101439940907011215701899456014662071926451200000,829726696136835328433485294068646178065075200000,7898017947032824439221398664897536276307929600000
%N A272522 Number of set partitions of [n] into ten blocks with distinct sizes.
%H A272522 Alois P. Heinz, <a href="/A272522/b272522.txt">Table of n, a(n) for n = 55..1000</a>
%F A272522 a(n) = n! * [x^n*y^10] Product_{n>=1} (1+y*x^n/n!).
%p A272522 b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
%p A272522       or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n,i-1,t)+
%p A272522       `if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n,i))))
%p A272522     end:
%p A272522 a:= n-> b(n$2, 10):
%p A272522 seq(a(n), n=55..65);
%Y A272522 Column k=10 of A131632.
%K A272522 nonn
%O A272522 55,1
%A A272522 _Alois P. Heinz_, May 01 2016