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Sum of the n-th powers of the first n odd numbers.
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%I #104 Dec 10 2021 01:58:27

%S 1,10,153,3108,79225,2437006,87922513,3642188936,170423429841,

%T 8891285549650,511800291063721,32222868466588460,2202868653419747209,

%U 162509566498902542934,12868118600594014094625,1088626666242258867384848,97994054039441765759931169

%N Sum of the n-th powers of the first n odd numbers.

%F a(n) = Sum_{k=1..n} (2*k-1)^n.

%F a(n) ~ 2^n * n^n / (exp(1/2) - exp(-1/2)). - _Vaclav Kotesovec_, Dec 09 2021

%t Table[Sum[(2*k-1)^n, {k,1,n}], {n,1,20}] (* _Vaclav Kotesovec_, Dec 09 2021 *)

%o (PARI) a(n) = sum(k=1, n, (2*k-1)^n);

%Y Sum of the k-th powers of the first n odd numbers: A000290 (k=1), A000447 (k=2), A002593 (k=3), A002309 (k=4), A002594 (k=5), A259322 (k=6).

%Y Cf. A005408, A031971, A061787, A103438.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Dec 09 2021