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A282288
Expansion of (Sum_{k>=0} x^(k^4))^19.
3
1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 988, 513, 2926, 15505, 58140, 162792, 352716, 604656, 831402, 923780, 831402, 604656, 352716, 162792, 58140, 15504, 3078, 3249, 23275, 116280, 406980, 1058148, 2116296, 3325608, 4157010, 4157010, 3325608
OFFSET
0,2
COMMENTS
Number of ways to write n as an ordered sum of 19 fourth powers (A000583).
a(n) > 0 for all n >= 0.
Every natural number is the sum of at most 19 fourth powers (Balasubramanian, 1986).
LINKS
Eric Weisstein's World of Mathematics, Biquadratic Number
Eric Weisstein's World of Mathematics, Waring's Problem
FORMULA
G.f.: (Sum_{k>=0} x^(k^4))^19.
MATHEMATICA
nmax = 42; CoefficientList[Series[Sum[x^k^4, {k, 0, nmax}]^19, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Feb 12 2017
STATUS
approved