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A299195 Number of ordered ways of writing n^4 as a sum of n fourth powers of positive integers.

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%I A299195 #10 Feb 16 2025 08:33:53
%S A299195 1,1,0,0,0,30,6,0,0,0,360,157080,0,12586860,0,714233520,579379361,
%T A299195 48062263014,46026944529624,759085890469938,170947379002578290,
%U A299195 3331302954541376850,479526242126281889924,11322897238957194004884,1341983461418984670506352,31585668052999315295625900
%N A299195 Number of ordered ways of writing n^4 as a sum of n fourth powers of positive integers.
%H A299195 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>
%F A299195 a(n) = [x^(n^4)] (Sum_{k>=1} x^(k^4))^n.
%e A299195 a(6) = 6 because we have [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] and [16, 256, 256, 256, 256, 256].
%t A299195 a[0] = 1; a[n_] := Coefficient[Sum[x^k^4, {k, n-1}]^n // Expand, x, n^4]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 25}] (* _Jean-François Alcover_, Feb 05 2018 *)
%Y A299195 Cf. A000583, A046042, A259793, A298330, A298672, A298859, A299169.
%K A299195 nonn
%O A299195 0,6
%A A299195 _Ilya Gutkovskiy_, Feb 04 2018
%E A299195 More terms from _Alois P. Heinz_, Feb 04 2018