A016863 -id:A016863 - cp's OEIS frontend

A377559 Decimal expansion of Sum_{k>=0} 1/(5*k + 1)^3.

1, 0, 0, 5, 9, 1, 2, 1, 4, 4, 4, 5, 7, 7, 4, 3, 7, 3, 2, 2, 3, 6, 7, 9, 2, 3, 6, 0, 1, 4, 7, 0, 0, 1, 4, 4, 8, 2, 5, 4, 9, 3, 6, 1, 1, 2, 0, 6, 4, 0, 2, 4, 5, 8, 2, 4, 7, 0, 3, 3, 3, 9, 6, 5, 0, 7, 1, 0, 0, 0, 5, 7, 4, 8, 0, 7, 3, 9, 3, 4, 6, 2, 0, 2, 7, 7, 4, 1, 1, 7, 8, 1, 0, 7, 3, 1, 2, 0, 3, 6

Offset: 1

Stefano Spezia, Nov 01 2024

			1.00591214445774373223679236014700144825493611206...

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 32.

Cf. A016861, A016863, A233091, A377557, A377558, A377560.

RealDigits[-PolyGamma[2,1/5]/250,10,100][[1]]

Equals -psi''(1/5)/250 (see Shamos).

A016864 a(n) = (5*n + 1)^4.

Original entry on oeis.org

1, 1296, 14641, 65536, 194481, 456976, 923521, 1679616, 2825761, 4477456, 6765201, 9834496, 13845841, 18974736, 25411681, 33362176, 43046721, 54700816, 68574961, 84934656, 104060401, 126247696

Offset: 0

N. J. A. Sloane

			a(0) = (5*0 + 1)^4 = 1.

Amiram Eldar, Table of n, a(n) for n = 0..10000
Eric Weisstein's MathWorld, Polygamma Function.
Wikipedia, Polygamma Function.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A016861, A016862, A016863.

Table[(5*n + 1)^4, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020*)
LinearRecurrence[{5,-10,10,-5,1},{1,1296,14641,65536,194481},30] (* Harvey P. Dale, Jul 22 2021 *)

Sum_{n>=0} 1/a(n) = polygamma(3, 1/5)/3750. - Amiram Eldar, Oct 02 2020
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Wesley Ivan Hurt, Oct 02 2020
G.f.: -(1+1291*x+8171*x^2+5281*x^3+256*x^4)/(-1+x)^5. - Wesley Ivan Hurt, Oct 02 2020

cp's OEIS Frontend

A377559 Decimal expansion of Sum_{k>=0} 1/(5*k + 1)^3.

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