OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..924
FORMULA
a(n) = [x^(2n)] (Sum_{j>=1} prime(j)*x^j)^n.
a(n) = A340991(2n,n).
MAPLE
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, ithprime(n+1),
(q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..23);
MATHEMATICA
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}]]]];
a[n_] := b[n, n];
a /@ Range[0, 23] (* Jean-François Alcover, Feb 04 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 01 2021
STATUS
approved