login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306765 Decimal expansion of a limit_{n->inf} n^A001620 / n! * Product_{j=1..n} Gamma(1/j). 3
2, 0, 3, 4, 4, 4, 8, 9, 4, 5, 4, 8, 7, 6, 1, 6, 4, 7, 7, 9, 8, 0, 3, 5, 5, 5, 3, 1, 8, 8, 6, 9, 0, 2, 6, 3, 5, 5, 9, 7, 9, 4, 3, 9, 8, 6, 3, 7, 0, 2, 3, 7, 6, 2, 6, 0, 0, 0, 5, 2, 8, 4, 1, 6, 5, 6, 5, 0, 0, 7, 8, 2, 7, 7, 5, 7, 1, 1, 3, 2, 4, 4, 5, 0, 2, 6, 5, 0, 4, 0, 6, 1, 3, 5, 0, 7, 5, 0, 2, 9, 1, 2, 7, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..297

FORMULA

Equals exp(-gamma^2 + Sum_{j>=2} (-1)^j*Zeta(j)^2/j), where gamma is the Euler-Mascheroni constant A001620.

Equals exp(-gamma^2 + A306769).

Equals limit_{n->infinity} n^(n*(2*n+1) + 2*gamma) * (2*Pi)^n * exp(1/6 + log(n)^2 - 2*n^2) / A306760(n).

EXAMPLE

2.0344489454876164779803555318869026355979439863702376260005284165650078277571...

MAPLE

evalf(exp(-gamma^2 + Sum((-1)^j*Zeta(j)^2/j, j=2..infinity)), 100);

MATHEMATICA

slogam = Table[Sum[LogGamma[1/j], {j, 1, n}], {n, 1, 1000}]; $MaxExtraPrecision = 1000; funs[n_] := E^slogam[[n]] * n^EulerGamma/n!; Do[Print[N[Sum[(-1)^(m + j) * funs[j*Floor[Length[slogam]/m]] * (j^(m - 1)/(j - 1)!/(m - j)!), {j, 1, m}], 80]], {m, 10, 100, 10}]

PROG

(PARI) exp(-Euler^2 + sumalt(j=2, (-1)^j*zeta(j)^2/j))

CROSSREFS

Cf. A001620, A231132, A303670, A306760, A306769.

Sequence in context: A101336 A300001 A137218 * A087819 A290820 A278029

Adjacent sequences:  A306762 A306763 A306764 * A306766 A306767 A306768

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 08 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)