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

1, 2, 7, 33, 226, 2420, 31221, 525917, 9960028, 228028812, 6582873441, 203832844657, 7522104144920, 307994276065974, 13236129969377405, 621482119947376921, 32898794005805573210, 1939157848567313376490, 118255213619653849652599, 7917287291057332412711339

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Formula

a(n) = Sum_{j=0..floor(n/2)} A096334(n-j,j).

a(n) mod 2 = A021913(n) for n>=1.

Example

a(0) = 1.
a(1) = 2.
a(2) = 2*3 + 1 = 7.
a(3) = 2*3*5 + 3 = 33.
a(4) = 2*3*5*7 + 3*5 + 1 = 226.
a(5) = 2*3*5*7*11 + 3*5*7 + 5 = 2420.

Maple

b:= proc(n, k) option remember;
     `if`(n=k, 1, b(n-1, k)*ithprime(n))
    end:
a:= n-> add(b(n-j, j), j=0..n/2):
seq(a(n), n=0..20);

Mathematica

b[n_, k_] := b[n, k] = If[n == k, 1, b[n - 1, k]*Prime[n]];
a[n_] := Sum[b[n - j, j], {j, 0, n/2}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 08 2022, after Alois P. Heinz *)

Crossrefs

Antidiagonal sums of A096334.

Cf. A000040, A002110, A021913.

Sequence in context: A144005 A232690 A143889 * A241767 A222940 A227120

Adjacent sequences: A350755 A350756 A350757 * A350759 A350760 A350761

Keyword

nonn

Author

Alois P. Heinz, Jan 21 2022

Status

approved