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A299169 Number of ordered ways of writing n^4 as a sum of n fourth powers of nonnegative integers.

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%I A299169 #9 Feb 16 2025 08:33:53
%S A299169 1,1,2,3,4,35,12,217,8,58473,7930,572891,5556,122985733,5175184,
%T A299169 22299917655,579379377,743262257063,56837361641571,1395217574459461,
%U A299169 375984668290604635,6891217627023943395,1297848300143194333479,26228516046396477884555,3686440821146129098950735
%N A299169 Number of ordered ways of writing n^4 as a sum of n fourth powers of nonnegative integers.
%H A299169 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>
%F A299169 a(n) = [x^(n^4)] (Sum_{k>=0} x^(k^4))^n.
%e A299169 a(6) = 12 because we have [1296, 0, 0, 0, 0, 0], [256, 256, 256, 256, 256, 16], [256, 256, 256, 256, 16, 256], [256, 256, 256, 16, 256, 256], [256, 256, 16, 256, 256, 256], [256, 16, 256, 256, 256, 256], [16, 256, 256, 256, 256, 256], [0, 1296, 0, 0, 0, 0], [0, 0, 1296, 0, 0, 0], [0, 0, 0, 1296, 0, 0], [0, 0, 0, 0, 1296, 0] and [0, 0, 0, 0, 0, 1296].
%Y A299169 Cf. A000583, A046042, A259793, A298329, A298671, A298859, A298989.
%K A299169 nonn
%O A299169 0,3
%A A299169 _Ilya Gutkovskiy_, Feb 04 2018
%E A299169 More terms from _Jinyuan Wang_, Dec 21 2021