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A258232 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k) dx. 16
3, 6, 8, 4, 1, 2, 5, 3, 5, 9, 3, 1, 4, 3, 3, 6, 5, 2, 3, 2, 1, 3, 1, 6, 5, 9, 7, 3, 2, 7, 8, 5, 1, 0, 1, 5, 0, 1, 4, 2, 4, 1, 3, 0, 3, 9, 2, 8, 8, 1, 9, 9, 6, 8, 3, 0, 3, 6, 1, 5, 8, 0, 6, 6, 8, 2, 8, 1, 4, 7, 3, 0, 0, 8, 8, 9, 0, 3, 4, 3, 9, 2, 9, 8, 9, 0, 6, 3, 4, 4, 2, 4, 2, 4, 1, 4, 9, 9, 2, 1, 7, 6, 7, 1, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..105.

Vaclav Kotesovec, The integration of q-series

FORMULA

Equals 8*Pi*sqrt(3/23) * sinh(sqrt(23)*Pi/6) / (2*cosh(sqrt(23)*Pi/3) - 1).

EXAMPLE

0.3684125359314336523213165973278510150142413039288199683036158...

MAPLE

evalf(8*sqrt(3/23)*Pi*sinh(sqrt(23)*Pi/6)/(2*cosh(sqrt(23)*Pi/3)-1), 123);

evalf(Sum((-1)^n/((3*n-1)*n/2 + 1), n=-infinity..infinity), 123);

MATHEMATICA

RealDigits[N[8*Sqrt[3/23]*Pi*Sinh[Sqrt[23]*Pi/6] / (2*Cosh[Sqrt[23]*Pi/3]-1), 120]][[1]]

CROSSREFS

Cf. A010815, A242168, A258229, A258230, A258408.

Cf. A258406 (m=2), A258407 (m=3), A258404 (m=4), A258405 (m=5).

Sequence in context: A200340 A108369 A010621 * A296568 A294095 A096416

Adjacent sequences:  A258229 A258230 A258231 * A258233 A258234 A258235

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, May 24 2015

STATUS

approved

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Last modified June 21 23:16 EDT 2018. Contains 305646 sequences. (Running on oeis4.)