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%I #6 Jan 16 2020 19:56:31
%S 1,1,-1,-7,19,229,-1009,-17263,105211,2332141,-18148681,-494079367,
%T 4678377859,151026527989,-1684778524129,-62909200846303,
%U 807879476432971,34252260613710781,-497629527847938361,-23615390533271153527,382915997208515638099,20108383384185058286149
%N a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n - k) * binomial(n,k) * a(k-1) * a(n-k).
%t a[n_] := a[n] = Sum[(-1)^(n - k) Binomial[n, k] a[k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 21}]
%o (PARI) seq(n)={my(a=vector(n+1)); a[1]=1; for(n=1, #a-1, a[1+n]=sum(k=1,n, (-1)^(n - k) * binomial(n,k) * a[k] * a[1+n-k])); a} \\ _Andrew Howroyd_, Jan 16 2020
%Y Cf. A000182, A001147, A090192.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Jan 16 2020
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