The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A346405 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A346405

a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k)^2 * k!).
(history; published version)

#5 by Susanna Cuyler at Thu Jul 15 21:21:08 EDT 2021

STATUS

proposed

approved

#4 by Ilya Gutkovskiy at Thu Jul 15 16:28:52 EDT 2021

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Thu Jul 15 15:39:25 EDT 2021

CROSSREFS

Cf. A001819, A002104, A002720, A061573, A346409.

#2 by Ilya Gutkovskiy at Thu Jul 15 15:32:56 EDT 2021

NAME

allocated for Ilya Gutkovskiy

a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k)^2 * k!).

DATA

0, 1, 5, 31, 268, 3476, 70656, 2202432, 98622336, 5954736384, 463100042880, 44924476970880, 5308404719823360, 749930460864929280, 124754522068412651520, 24129984694192721971200, 5368254991077002482483200, 1360938718277588430567014400, 389980903967231535140578099200

OFFSET

0,3

FORMULA

Sum_{n>=0} a(n) * x^n / (n!)^2 = polylog(2,x) * exp(x).

MATHEMATICA

Table[(n!)^2 Sum[1/((n - k)^2 k!), {k, 0, n - 1}], {n, 0, 18}]

nmax = 18; CoefficientList[Series[PolyLog[2, x] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A001819, A002104, A002720, A061573.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Jul 15 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Thu Jul 15 15:32:56 EDT 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved