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A258412 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k)^k dx. 0
2, 9, 8, 7, 8, 3, 3, 6, 5, 1, 0, 6, 5, 6, 7, 2, 9, 8, 7, 7, 0, 9, 5, 3, 7, 7, 2, 1, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Integral_{x=0..1} Product_{k=1..n} (1+x^k)^k dx ~ 3*2^(n*(n+1)/2 + 1)/n^3.

Integral_{x=0..1} Product_{k=1..n} (1+x^k)   dx ~ 2^(n+2)/n^2.

Integral_{x=0..1} Product_{k>=1}   (1-x^k)   dx = A258232 = 0.3684125359314...

Integral_{x=0..1} Product_{k=1..n} (1-x^k)^n dx ~ 1/n.

Integral_{x=0..1} Product_{k=1..n} (1+x^k)^n dx ~ 2^(n^2 + 2)/n^3.

LINKS

Table of n, a(n) for n=0..29.

Vaclav Kotesovec, The integration of q-series

EXAMPLE

0.298783365106567298770953772114...

CROSSREFS

Cf. A073592, A258232.

Sequence in context: A076219 A077601 A090930 * A151927 A046017 A155909

Adjacent sequences:  A258409 A258410 A258411 * A258413 A258414 A258415

KEYWORD

nonn,cons,more

AUTHOR

Vaclav Kotesovec, May 29 2015

STATUS

approved

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Last modified June 13 10:36 EDT 2021. Contains 344988 sequences. (Running on oeis4.)