A398396 - OEIS

A398396

Decimal expansion of Sum_{k>=1} 4^k * H(k) / (k^3 * binomial(2*k,k)), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2nd ed., 2023, section 4.9.3, pp. 365-367, eq. (4.169).

Index entries for sequences related to harmonic numbers.

FORMULA

Equals zeta(4) + 8*log(2)^2*zeta(2) - log(2)^4/3 - 8*Li_4(1/2).

EXAMPLE

3.188053948370552153757444514206146247588638821704943...

MATHEMATICA