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a(n) = n! * [x^n] exp(((1+x)^(n+1) - 1)/(n+1)).
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%I #9 Oct 22 2017 07:27:11

%S 1,1,3,16,145,2046,40831,1078288,36229761,1508861980,76260702331,

%T 4591005777216,323906453871793,26419909067594056,2463658914613015575,

%U 260204512488337862656,30878562368653933102081,4088281211853327516484368,600094288103991706472584051

%N a(n) = n! * [x^n] exp(((1+x)^(n+1) - 1)/(n+1)).

%H Seiichi Manyama, <a href="/A294003/b294003.txt">Table of n, a(n) for n = 0..281</a>

%Y Main diagonal of A293991.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 21 2017