The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A373855 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A373855

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

#10 by Michael De Vlieger at Wed Jun 19 09:28:17 EDT 2024

STATUS

proposed

approved

#9 by Stefano Spezia at Wed Jun 19 09:03:48 EDT 2024

STATUS

editing

proposed

#8 by Stefano Spezia at Wed Jun 19 09:03:42 EDT 2024

MATHEMATICA

nmax=15; Range[0, nmax]!CoefficientList[Series[Sum[(-Log[1 - k*x])^k / k, {k, nmax}], {x, 0, nmax}], x] (* Stefano Spezia, Jun 19 2024 *)

STATUS

proposed

editing

#7 by Seiichi Manyama at Wed Jun 19 08:32:32 EDT 2024

STATUS

editing

proposed

#6 by Seiichi Manyama at Wed Jun 19 06:19:01 EDT 2024

CROSSREFS

Cf. A092552, A244585, A373857.

#5 by Seiichi Manyama at Wed Jun 19 05:49:26 EDT 2024

NAME

a(n) = Sum_{k=1..n} (-1)^(n-k) * k! * k^(n-1) * |Stirling1(n,k)|.

PROG

(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*k!*k^(n-1)*abs(stirling(n, k, 1)));

#4 by Seiichi Manyama at Wed Jun 19 05:45:02 EDT 2024

CROSSREFS

Cf. A320096.

#3 by Seiichi Manyama at Wed Jun 19 05:43:21 EDT 2024

CROSSREFS

Cf. A003713, A373856.

#2 by Seiichi Manyama at Wed Jun 19 05:41:09 EDT 2024

NAME

allocated for Seiichi Manyama

a(n) = Sum_{k=1..n} (-1)^(n-k) * k! * k^(n-1) * Stirling1(n,k).

DATA

0, 1, 5, 80, 2690, 155074, 13658386, 1706098008, 286888266696, 62485391828448, 17112247116585744, 5755236604915060944, 2331975856351260982848, 1120439648590390138640304, 629855675998212293917375344, 409557081242059531918330384896

OFFSET

0,3

FORMULA

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

PROG

(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*k!*k^(n-1)*stirling(n, k, 1));

CROSSREFS

Cf. A003713.

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Jun 19 2024

STATUS

approved

editing

#1 by Seiichi Manyama at Wed Jun 19 05:41:09 EDT 2024

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved