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A299195
Number of ordered ways of writing n^4 as a sum of n fourth powers of positive integers.
3
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
0,6
LINKS
Eric Weisstein's World of Mathematics, Biquadratic Number
FORMULA
a(n) = [x^(n^4)] (Sum_{k>=1} x^(k^4))^n.
EXAMPLE
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].
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 *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 04 2018
EXTENSIONS
More terms from Alois P. Heinz, Feb 04 2018
STATUS
approved