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A109398 a(n) = (1/n!)*Sum_{k=0..n} (n+k)!. 1
1, 3, 16, 145, 1926, 33649, 726328, 18636561, 553680370, 18684924841, 705833193924, 29502690532393, 1351724235304366, 67359683340291105, 3627011494019437936, 209846445862386234529, 12982402818188717219658 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) ~ 2^(2*n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Nov 27 2017

MATHEMATICA

Table[Sum[Binomial[n+k, k]k!, {k, 0, n}], {n, 0, 100}] (* Emanuele Munarini, Sep 20 2016 *)

PROG

(Maxima) makelist(sum(binomial(n+k, k)*k!, k, 0, n), n, 0, 12); // Emanuele Munarini, Sep 20 2016 //

CROSSREFS

Cf. A111686.

Sequence in context: A062874 A321239 A349969 * A294003 A006058 A121588

Adjacent sequences: A109395 A109396 A109397 * A109399 A109400 A109401

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 26 2005

STATUS

approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)