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A350895 a(n) = 1 + a(n-1) * prime(n), starting a(0) = 1.

%I A350895 #32 Jul 30 2023 16:04:30
%S A350895 1,3,10,51,358,3939,51208,870537,16540204,380424693,11032316098,
%T A350895 342001799039,12654066564444,518816729142205,22309119353114816,
%U A350895 1048528609596396353,55572016308609006710,3278748962207931395891,200003686694683815149352,13400247008543815615006585
%N A350895 a(n) = 1 + a(n-1) * prime(n), starting a(0) = 1.
%C A350895 a(n) is the sum of all (j+1)-th products of (n-j) successive primes for j=0..n: a(3) = 2*3*5 + 3*5 + 5 + 1 = ((1*2 + 1)*3 + 1)*5 + 1 = 51.
%H A350895 Alois P. Heinz, <a href="/A350895/b350895.txt">Table of n, a(n) for n = 0..350</a>
%F A350895 a(n) = Sum_{k=0..n} A096334(n,k) = Sum_{k=0..n} A002110(n)/A002110(k).
%F A350895 a(n) mod 2 = A135528(n+1).
%p A350895 a:= proc(n) option remember;
%p A350895      `if`(n=0, 1, 1+a(n-1)*ithprime(n))
%p A350895     end:
%p A350895 seq(a(n), n=0..23);
%t A350895 Nest[Append[#1, 1 + #1[[-1]] Prime[#2]] & @@ {#, Length@ #} &, {1}, 19] (* _Michael De Vlieger_, Jan 22 2022 *)
%t A350895 nxt[{n_,a_}]:={n+1,a Prime[n+1]+1}; NestList[nxt,{0,1},20][[;;,2]] (* _Harvey P. Dale_, Jul 30 2023 *)
%o A350895 (PARI) a(n) = if (n, 1 + a(n-1)*prime(n), 1); \\ _Michel Marcus_, Jan 22 2022
%Y A350895 Row sums of A096334.
%Y A350895 Cf. A000040, A002110, A135528.
%K A350895 nonn
%O A350895 0,2
%A A350895 _Alois P. Heinz_, Jan 21 2022