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A350758 Sum of all (j+1)-th products of (n-2j) successive primes for j=0..floor(n/2).

%I A350758 #32 May 08 2022 08:45:23
%S A350758 1,2,7,33,226,2420,31221,525917,9960028,228028812,6582873441,
%T A350758 203832844657,7522104144920,307994276065974,13236129969377405,
%U A350758 621482119947376921,32898794005805573210,1939157848567313376490,118255213619653849652599,7917287291057332412711339
%N A350758 Sum of all (j+1)-th products of (n-2j) successive primes for j=0..floor(n/2).
%H A350758 Alois P. Heinz, <a href="/A350758/b350758.txt">Table of n, a(n) for n = 0..350</a>
%F A350758 a(n) = Sum_{j=0..floor(n/2)} A096334(n-j,j).
%F A350758 a(n) mod 2 = A021913(n) for n>=1.
%e A350758 a(0) = 1.
%e A350758 a(1) = 2.
%e A350758 a(2) = 2*3 + 1 = 7.
%e A350758 a(3) = 2*3*5 + 3 = 33.
%e A350758 a(4) = 2*3*5*7 + 3*5 + 1 = 226.
%e A350758 a(5) = 2*3*5*7*11 + 3*5*7 + 5 = 2420.
%p A350758 b:= proc(n, k) option remember;
%p A350758      `if`(n=k, 1, b(n-1, k)*ithprime(n))
%p A350758     end:
%p A350758 a:= n-> add(b(n-j, j), j=0..n/2):
%p A350758 seq(a(n), n=0..20);
%t A350758 b[n_, k_] := b[n, k] = If[n == k, 1, b[n - 1, k]*Prime[n]];
%t A350758 a[n_] := Sum[b[n - j, j], {j, 0, n/2}];
%t A350758 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, May 08 2022, after _Alois P. Heinz_ *)
%Y A350758 Antidiagonal sums of A096334.
%Y A350758 Cf. A000040, A002110, A021913.
%K A350758 nonn
%O A350758 0,2
%A A350758 _Alois P. Heinz_, Jan 21 2022