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%I #6 May 13 2022 10:00:34
%S 3,-4,-8,-26,-52,-126,-320,-1214,-2016,-7068,-16064,-48142,-122552,
%T -390574,-903176,-3549556,-7597004,-22902332,-61172890,-198872948,
%U -486889660,-1555059566,-4093173788,-12448334478,-33815484714,-105268420776,-279683446078,-894795490384,-2366564864546
%N Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} prime(n+1)*x^n.
%t A[m_, n_] := A[m, n] = Which[m == 1, Prime[n + 1], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 29]
%Y Cf. A006005, A065091, A147557, A305882, A353605, A353606, A353951.
%K sign
%O 1,1
%A _Ilya Gutkovskiy_, May 12 2022