A014345 Exponential convolution of primes with themselves.

4, 12, 38, 118, 362, 1082, 3166, 8910, 24426, 64226, 165262, 413418, 1021362, 2490686, 6009150, 14401410, 34098042, 80281962, 187356750, 432549154, 992941250, 2256712462, 5088826238, 11408805862, 25425739346, 56383362854, 124565557898, 274390550594

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A014347, A014352.

Programs

Magma

[&+[NthPrime(k+1)*NthPrime(n-k+1)*Binomial(n, k): k in [0..n]]: n in [0..30]]; // Vincenzo Librandi, Jun 07 2019

Maple

a:= proc(n) option remember; (p-> add(
      p(j+1)*p(n-j+1)*binomial(n, j), j=0..n))(ithprime)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 10 2018

Mathematica

a[n_] := Sum[Prime[j + 1] Prime[n - j + 1] Binomial[n, j], {j, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 05 2018, from Maple *)

PARI

{a(n) = sum(j=0,n, binomial(n,j)*prime(j+1)*prime(n-j+1))}; \\ G. C. Greubel, Jun 07 2019

Sage

[sum(binomial(n,j)*nth_prime(j+1)*nth_prime(n-j+1) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 07 2019

Formula

E.g.f.: (Sum_{k>=0} prime(k+1)*x^k/k!)^2. - Ilya Gutkovskiy, Mar 10 2018

a(n) = Sum_{j=0..n} binomial(n,j)*prime(j+1)*prime(n-j+1). - G. C. Greubel, Jun 07 2019