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A014351 Four-fold exponential convolution of primes with themselves (divided by 8).

%I A014351 #12 Jul 08 2025 05:37:08
%S A014351 2,12,74,460,2861,17722,109037,665020,4014521,23954342,141123193,
%T A014351 820074040,4697137637,26504081542,147300078809,806343223508,
%U A014351 4349380581953,23130233881414,121379963732665,629130600591920,3224186845616653,16354295398317790,82187373706636505
%N A014351 Four-fold exponential convolution of primes with themselves (divided by 8).
%H A014351 Alois P. Heinz, <a href="/A014351/b014351.txt">Table of n, a(n) for n = 0..1000</a>
%p A014351 b:= proc(n, k) option remember; `if`(k=1, ithprime(n+1), add(
%p A014351       b(j, floor(k/2))*b(n-j, ceil(k/2))*binomial(n, j), j=0..n))
%p A014351     end:
%p A014351 a:= n-> b(n, 4)/8:
%p A014351 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jun 07 2018
%t A014351 b[n_, k_] := b[n, k] = If[k==1, Prime[n+1], Sum[b[j, Floor[k/2]] b[n-j, Ceiling[k/2]] Binomial[n, j], {j, 0, n}]];
%t A014351 a[n_] := b[n, 4]/8;
%t A014351 a /@ Range[0, 30] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%Y A014351 Cf. A014352.
%K A014351 nonn
%O A014351 0,1
%A A014351 _N. J. A. Sloane_