A181426 Numerator of Sum_{k=1..n} k^4 / Product_{k=1..n} k^4.

1, 17, 49, 59, 979, 91, 167, 731, 5111, 517, 1817, 6071, 109, 18241, 22289, 2771, 131, 28823, 67, 51619, 11911, 34891, 15557, 257, 1949, 22313, 2267, 14123, 153931, 5273999, 1, 3167, 45091, 3569, 268309, 126947, 4217, 127, 369641, 201679, 85739

Offset: 1

Author

Alexander Adamchuk, Oct 18 2010

Keywords

• nonn
• frac

Comments

a(n) = 1 for n = {1, 31, 59, 94, 104, 122, 133, 181, 206, 223, ...} = A166604.

Examples

			The first few fractions are 1, 17/16, 49/648, 59/55296, 979/207360000, 91/10749542400, 167/23044331520000, ... = A181426/A334734.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A090585 = Numerator of Sum/Product of first n numbers.

Cf. A125294 = Numerator of Sum/Product of squares of first n numbers.

Cf. A166604, A334734 (denominators).

Programs

Mathematica

Table[Numerator[Sum[ k^4, {k, 1, n}] / Product[k^4, {k, 1, n}]], {n, 1, 100}]
With[{c=Range[50]^4},Numerator[Accumulate[c]/FoldList[Times,c]]] (* Harvey P. Dale, Jul 03 2025 *)

PARI

a(n) = numerator(sum(k=1, n, k^4)/prod(k=1, n, k^4)); \\ Michel Marcus, May 09 2020