The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A330493 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A330493

a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * tau(k), where tau = A000005.
(history; published version)

#18 by Joerg Arndt at Mon Dec 16 11:40:57 EST 2019

STATUS

reviewed

approved

#17 by Hugo Pfoertner at Mon Dec 16 11:31:29 EST 2019

STATUS

proposed

reviewed

#16 by Michel Marcus at Mon Dec 16 11:29:48 EST 2019

STATUS

editing

proposed

#15 by Michel Marcus at Mon Dec 16 11:29:44 EST 2019

PROG

(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1)*(k-1)!*numdiv(k)); \\ Michel Marcus, Dec 16 2019

STATUS

approved

editing

#14 by Vaclav Kotesovec at Mon Dec 16 08:01:04 EST 2019

STATUS

editing

approved

#13 by Vaclav Kotesovec at Mon Dec 16 08:00:59 EST 2019

LINKS

Vaclav Kotesovec, <a href="/A330493/b330493.txt">Table of n, a(n) for n = 1..400</a>

STATUS

approved

editing

#12 by Vaclav Kotesovec at Mon Dec 16 05:56:38 EST 2019

STATUS

editing

approved

#11 by Vaclav Kotesovec at Mon Dec 16 05:56:30 EST 2019

FORMULA

E.g.f.: -Sum_{k>=1} log(1 - log(1/(1 - x))^k) / k.

STATUS

approved

editing

#10 by Vaclav Kotesovec at Mon Dec 16 05:48:48 EST 2019

STATUS

editing

approved

#9 by Vaclav Kotesovec at Mon Dec 16 05:47:09 EST 2019

MATHEMATICA

nmax = 20; Rest[CoefficientList[Series[-Sum[Log[1 - Log[1/(1 - x)]^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!]

STATUS

approved

editing