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A242228 a(n) = Sum_{k=1..n} k^(2*n-1) * k! * StirlingS2(n,k). 3
1, 17, 1651, 473741, 300257371, 355743405917, 706872713310331, 2182548723605418941, 9894910566488309801851, 63052832687428562206049117, 545439670961897317869306191611, 6226501736967631584015448186252541, 91619831483112536750163352484302283131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..160

FORMULA

a(n) ~ c * d^n * (n!)^3 / n^2, where d = r^3*(1+exp(2/r)) = 7.8512435106631367719817991716164612615296980032514..., r = 0.94520217245242431308104743874492469552738... is the root of the equation (1+exp(-2/r))*LambertW(-exp(-1/r)/r) = -1/r, and c = 0.15095210978787998524366903417512193343948127919...

MATHEMATICA

Table[Sum[k^(2*n-1) * k! * StirlingS2[n, k], {k, 1, n}], {n, 1, 20}]

CROSSREFS

Cf. A220179, A229260.

Sequence in context: A133590 A227887 A144571 * A222905 A071826 A055414

Adjacent sequences:  A242225 A242226 A242227 * A242229 A242230 A242231

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 08 2014

STATUS

approved

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Last modified May 25 02:55 EDT 2022. Contains 354047 sequences. (Running on oeis4.)