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a(n) = A304400(n) / n^2 for n >= 1.
2

%I #5 May 25 2018 17:20:34

%S 1,2,17,296,8205,322412,16861408,1129044208,94262593881,9617095872812,

%T 1179417144559337,171422055924510232,29164680268271517644,

%U 5744954740594875376712,1297633915706481674014856,333220154688593666676579264,96542160783658837442386115393,31344432027934429150200553978812

%N a(n) = A304400(n) / n^2 for n >= 1.

%H Paul D. Hanna, <a href="/A304857/b304857.txt">Table of n, a(n) for n = 1..300</a>

%o (PARI) {a(n) = my(A=[1], m); for(i=1, n, A=concat(A, 0); m=#A; A[m] = Vec( exp( (m-1)^2 * x * Ser(A) ) * (2 - Ser(A)) )[m] ); A[n+1]/n^2}

%o for(n=1, 20, print1(a(n), ", "))

%Y Cf. A304400.

%K nonn

%O 1,2

%A _Paul D. Hanna_, May 25 2018