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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-Fran├žois 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 November 13 15:41 EST 2019. Contains 329106 sequences. (Running on oeis4.)