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Main diagonal of A045847.
11

%I #17 Mar 25 2023 08:10:31

%S 1,1,1,1,5,21,61,141,309,766,2191,6436,18041,48348,128311,347166,

%T 960197,2674883,7413514,20411986,56130675,154907229,429349768,

%U 1192532452,3312339849,9196063371,25538113056,70994900341,197595884071,550414483911,1533911418946

%N Main diagonal of A045847.

%C a(n) is the number of representations of n as a sum of n squares of nonnegative integers.

%H Seiichi Manyama, <a href="/A287617/b287617.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = [x^n] (1 + theta_3(x))^n/2^n, where theta_() is the Jacobi theta function. - _Ilya Gutkovskiy_, Jan 17 2018

%F a(n) ~ c * d^n / sqrt(n), where d = 2.83312434251238... and c = 0.229098651125... - _Vaclav Kotesovec_, Mar 25 2023

%Y Cf. A045847.

%K nonn

%O 0,5

%A _Seiichi Manyama_, May 28 2017