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 A259793 Number of partitions of n^4 into fourth powers. 14
 1, 1, 2, 7, 36, 253, 1886, 14800, 118238, 955639, 7750456, 62777522, 506272363, 4056634991, 32252971687, 254209569990, 1985108901344, 15352968310930, 117579612410477, 891596419221856, 6694250497509934, 49768995849050468, 366423320400440927, 2671969175372760210 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..63 (terms 0..45 from Alois P. Heinz) H. L. Fisher, Letter to N. J. A. Sloane, Mar 16 1989 G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatory analysis, Proceedings of the London Mathematical Society, 2, XVI, 1917, p. 373. FORMULA a(n) = [x^(n^4)] Product_{j>=1} 1/(1-x^(j^4)). - Alois P. Heinz, Jul 10 2015 a(n) = A046042(n^4). - Vaclav Kotesovec, Aug 19 2015 a(n) ~ exp(5 * (Gamma(1/4)*Zeta(5/4))^(4/5) * n^(4/5) / 2^(16/5)) * (Gamma(1/4)*Zeta(5/4))^(4/5) / (2^(47/10) * sqrt(5) * Pi^(5/2) * n^(26/5)) [after Hardy & Ramanujan, 1917]. - Vaclav Kotesovec, Dec 29 2016 MAPLE b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,       b(n, i-1) +`if`(i^4>n, 0, b(n-i^4, i)))     end: a:= n-> b(n^4, n): seq(a(n), n=0..23);  # Alois P. Heinz, Jul 10 2015 MATHEMATICA \$RecursionLimit = 10^4; b[n_, i_] := b[n, i] = If[n==0 || i==1, 1, b[n, i-1] + If[i^4>n, 0, b[n-i^4, i]]]; a[n_] := b[n^4, n];  Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Dec 06 2016 after Alois P. Heinz *) CROSSREFS A row of the array in A259799. Cf. A001156, A003108, A046042. Cf. A037444, A259792. Sequence in context: A034430 A143805 A249637 * A112293 A090352 A123549 Adjacent sequences:  A259790 A259791 A259792 * A259794 A259795 A259796 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 06 2015 EXTENSIONS More terms from Alois P. Heinz, Jul 10 2015 STATUS approved

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Last modified April 15 12:35 EDT 2021. Contains 342977 sequences. (Running on oeis4.)