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a(n) = n! * [x^n] exp(Sum_{j>=1} j^(n-1)*x^j).
2

%I #12 Oct 17 2017 05:19:53

%S 1,1,5,79,3049,281781,62813281,31485039139,34744132717841,

%T 87021427208179753,478223788295847736801,5632387976229387238588911,

%U 146556226850373293041283537497,8264489999577847335581419448796253,987463694910250882031042208037752864641

%N a(n) = n! * [x^n] exp(Sum_{j>=1} j^(n-1)*x^j).

%H Vaclav Kotesovec, <a href="/A293786/b293786.txt">Table of n, a(n) for n = 0..76</a>

%F log(a(n)) ~ exp(-1) * n^2. - _Vaclav Kotesovec_, Oct 17 2017

%t Table[n!*SeriesCoefficient[Exp[Sum[j^(n-1)*x^j, {j, 1, n}]], {x, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 17 2017 *)

%Y Main diagonal of A293785.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 16 2017