A255438 Decimal expansion of a constant related to A255359.

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

Offset

1,1

Links

Table of n, a(n) for n=1..88.

Formula

Equals limit n->infinity (Product_{k=0..n} (k^4)!) / (n^(1 + 28*n/15 + 4*n^3/3 + 2*n^4 + 4*n^5/5) * (2*Pi)^(n/2) / exp(19*n/9 + n^4/2 + 9*n^5/25)).

Equals 2*Pi*exp(-3*Zeta(5)/Pi^4) * Product_{n>=1} ((n^4)!/stirling(n^4)), where stirling(n^4) = sqrt(2*Pi) * n^(4*n^4 + 2) / exp(n^4) is the Stirling approximation of (n^4)! and Zeta(5) = A013663. - Vaclav Kotesovec, Apr 20 2016

Example

6.644987918706354049483118316737842660075362652005201561326290428710371...

Crossrefs

Cf. A255359, A255504, A255511, A255439.

Cf. A074962, A243262, A243263, A243264, A243265.

Sequence in context: A099405 A090966 A254153 * A200491 A245297 A371504

Adjacent sequences: A255435 A255436 A255437 * A255439 A255440 A255441

Keyword

nonn,cons

Author

Vaclav Kotesovec, Feb 24 2015

Status

approved