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A381515 a(n) = Sum_{j=1..n} Stirling2(n-1,j-1) * a(n-j) for n>=1, starting with a(0) = 1.

%I A381515 #12 Feb 26 2025 09:50:02
%S A381515 1,1,1,2,5,16,71,432,3446,35805,493247,9055817,219034736,6924788187,
%T A381515 287364757172,15747872749912,1138063678023858,107917571120653077,
%U A381515 13417659577126888599,2194989270698166806727,473329783091262653789042,134287984058139116699933228
%N A381515 a(n) = Sum_{j=1..n} Stirling2(n-1,j-1) * a(n-j) for n>=1, starting with a(0) = 1.
%H A381515 Alois P. Heinz, <a href="/A381515/b381515.txt">Table of n, a(n) for n = 0..129</a>
%p A381515 a:= proc(n) option remember; `if`(n=0, 1,
%p A381515       add(a(n-j)*Stirling2(n-1, j-1), j=1..n))
%p A381515     end:
%p A381515 seq(a(n), n=0..23);
%Y A381515 Cf. A000110, A008277, A048993, A308444.
%K A381515 nonn
%O A381515 0,4
%A A381515 _Alois P. Heinz_, Feb 25 2025