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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

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

Cf. A000040, A014347, A014352.

Sequence in context: A189499 A183159 A289809 * A006192 A149324 A149325

Adjacent sequences:  A014342 A014343 A014344 * A014346 A014347 A014348

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)