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A014345
Exponential convolution of primes with themselves.
7
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
0,1
LINKS
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
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 *)
PROG
(Magma) [&+[NthPrime(k+1)*NthPrime(n-k+1)*Binomial(n, k): k in [0..n]]: n in [0..30]]; // Vincenzo Librandi, Jun 07 2019
(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
CROSSREFS
KEYWORD
nonn
STATUS
approved