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A152006 Expansion of Product_{k > 0} (1 + f(k)*x^k), where f(1) = 1 and f(m) = prime(m-1) for m >= 2.

%I A152006 #18 Apr 14 2020 20:50:14
%S A152006 1,1,2,5,8,18,34,63,102,203,336,589,999,1675,2799,4768,7561,12224,
%T A152006 20513,31724,51621,81976,128560,199192,312536,482806,744847,1147952,
%U A152006 1755931,2649474,4051413,6069450,9105323,13747364,20335077,30508629,45198631
%N A152006 Expansion of Product_{k > 0} (1 + f(k)*x^k), where f(1) = 1 and f(m) = prime(m-1) for m >= 2.
%F A152006 a(n) = [x^n] Product_{k > 0} (1 + f(k)*x^k), where f(1) = 1 and f(m) = prime(m-1) for m >= 2.
%t A152006 f[n_] = If[n < 2, n, Prime[n - 1]];
%t A152006 P[x_, n_] := P[x, n] = Product[1 + f[m]*x^m, {m, 0, n}];
%t A152006 Take[CoefficientList[P[x, 37], x],37]
%t A152006 (* Program edited and corrected by _Petros Hadjicostas_, Apr 12 2020 *)
%Y A152006 Cf. A147557, A147654, A147655, A147665, A147869, A147871, A147880, A147953.
%K A152006 nonn
%O A152006 0,3
%A A152006 _Roger L. Bagula_, Nov 19 2008
%E A152006 Various sections edited by _Petros Hadjicostas_, Apr 12 2020