A367012 -id:A367012

Search: a367012 -id:a367012

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A367011

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

+10
3

1, 1, 3, 11, 51, 287, 1899, 14447, 124251, 1192127, 12623979, 146250287, 1840024251, 24983863967, 364140992139, 5670546353807, 93960923507931, 1650688221777407, 30646388716777899, 599565840087487727, 12328458398407260411

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..449

FORMULA

a(n) ~ Pi * n^(n+1) / exp(n).

a(n) ~ sqrt(Pi*n/2) * n!.

MATHEMATICA

Table[Sum[k! * k^(n-k), {k, 0, n}], {n, 1, 20}]

PROG

(PARI) a(n) = sum(k=0, n, k!*k^(n-k)); \\ Seiichi Manyama, Dec 31 2023

CROSSREFS

Cf. A026898, A112541, A367012.

Cf. A003422, A233449, A368555.

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Nov 01 2023

EXTENSIONS

a(0)=1 prepended by Seiichi Manyama, Dec 31 2023

STATUS

approved

A368573

a(n) = Sum_{k=0..n} k! * k^k.

+10
0

1, 2, 10, 172, 6316, 381316, 33973636, 4184630356, 680641979476, 141267789027796, 36429267789027796, 11425158161234192596, 4282251538636575402196, 1890291840090813125264596, 970616058694975134467523796, 573593232413546537634467523796, 386530943604347679737893326531796

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) ~ n! * n^n. - Vaclav Kotesovec, Jan 13 2024

PROG

(PARI) a(n) = sum(k=0, n, k!*k^k);

CROSSREFS

Partial sums of A061711.

Cf. A058006, A112368, A112370.

Cf. A367011, A367012, A368561.

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Dec 31 2023

STATUS

approved

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