A340990 - OEIS

%I #15 Feb 21 2023 10:48:21

%S 1,3,29,291,3121,34123,379853,4280251,48681569,557686227,6425630909,

%T 74384480019,864461820049,10079577033243,117859582680813,

%U 1381492094548651,16227770995740865,190979248798795427,2251327736286726749,26579050506578504195,314212180691846338801

%N a(n) is the (2n)-th term of the n-fold self-convolution of the primes.

%H Alois P. Heinz, <a href="/A340990/b340990.txt">Table of n, a(n) for n = 0..924</a>

%F a(n) = [x^(2n)] (Sum_{j>=1} prime(j)*x^j)^n.

%F a(n) = A340991(2n,n).

%p b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, ithprime(n+1),

%p       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..23);

%t b[n_, k_] := b[n, k] = If[k == 0, 1, If[k == 1, Prime[n + 1], With[{q = Quotient[k, 2]}, Sum[b[j, q] b[n - j, k - q], {j, 0, n}]]]];

%t a[n_] := b[n, n];

%t a /@ Range[0, 23] (* _Jean-François Alcover_, Feb 04 2021, after _Alois P. Heinz_ *)

%Y Cf. A000040, A309955, A340991.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 01 2021