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%I #21 Apr 26 2022 05:32:25
%S 1,14,197,3704,90309,2704470,95856025,3921108576,181756280697,
%T 9413656622446,538727822713277,33757715581666296,2298714540642445405,
%U 169016703698449309846,13345320616706684277361,1126219424250538393789824,101160070702700567996590513,9636001314414804672487492878
%N a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k - 1)^m.
%C a(3) = 197 and a(11) = 538727822713277 are primes.
%C p divides a(p+1) for primes p > 3.
%C a(2*k-1) is odd. a(2*k) is even. a(2^k) is divisible by 2^(2*k - 1) for k > 0.
%C Numbers n such that a(n) is divisible by n are listed in A124240.
%H T. D. Noe, <a href="/A124239/b124239.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k - 1)^m.
%F a(n) = n + Sum_{k=2..n} (2*k - 1)*((2*k - 1)^n - 1)/(2*(k - 1)).
%t Table[Sum[(2k-1)^m,{k,1,n},{m,1,n}],{n,1,20}]
%o (PARI) a(n) = sum(k=1, n, sum(m=1, n, (2*k - 1)^m)); \\ _Michel Marcus_, Apr 24 2022
%Y Cf. A124240, A124241.
%Y Cf. also A068563, A086787, A123855.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Oct 22 2006
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