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

1, 1, 0, 0, 0, 30, 6, 0, 0, 0, 360, 157080, 0, 12586860, 0, 714233520, 579379361, 48062263014, 46026944529624, 759085890469938, 170947379002578290, 3331302954541376850, 479526242126281889924, 11322897238957194004884, 1341983461418984670506352, 31585668052999315295625900

Offset: 0

Author

Ilya Gutkovskiy, Feb 04 2018

Keywords

• nonn

Examples

			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].
		

Links

• Eric Weisstein's World of Mathematics, Biquadratic Number

Crossrefs

Cf. A000583, A046042, A259793, A298330, A298672, A298859, A299169.

Programs

Mathematica

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 *)

Formula

a(n) = [x^(n^4)] (Sum_{k>=1} x^(k^4))^n.

Extensions

More terms from Alois P. Heinz, Feb 04 2018