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A030297 a(n) = n*(n + a(n-1)) with a(0)=0. 12
0, 1, 6, 27, 124, 645, 3906, 27391, 219192, 1972809, 19728190, 217010211, 2604122676, 33853594957, 473950329594, 7109254944135, 113748079106416, 1933717344809361, 34806912206568822, 661331331924807979 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Exponential convolution of factorials (A000142) and squares (A000290). - Vladimir Reshetnikov, Oct 07 2016

LINKS

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

FORMULA

a(n) = A019461(2n).

For n>=2, a(n) = floor(2*e*n! - n - 2). - Benoit Cloitre, Feb 16 2003

a(n) = sum_{k=0...n} (n! / k!) * k^2. - Ross La Haye, Sep 21 2004

E.g.f.: x*(1+x)*exp(x)/(1-x). - Vladeta Jovovic, Dec 01 2004

MAPLE

f := proc(n) options remember; if n <= 1 then n elif n = 2 then 6 else -n*(n-2)*f(n-3)+(n-3)*n*f(n-2)+3*n*f(n-1)/(n-1); fi; end;

MATHEMATICA

a=0; lst={a}; Do[a=(a+n)*n; AppendTo[lst, a], {n, 2*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2008 *)

RecurrenceTable[{a[0]==0, a[n]==n(n+a[n-1])}, a[n], {n, 20}] (* Harvey P. Dale, Oct 22 2011 *)

Round@Table[(2 E Gamma[n, 1] - 1) n, {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster - Vladimir Reshetnikov, Oct 07 2016 *)

CROSSREFS

Cf. A019461-A019464, A006183, A054096, A111063.

Sequence in context: A178935 A249792 A002912 * A045500 A109115 A038176

Adjacent sequences:  A030294 A030295 A030296 * A030298 A030299 A030300

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, "Urkonsaud_admin" (miti(AT)tula.sitek.net)

EXTENSIONS

Better description from Henry Bottomley, May 15 2000

STATUS

approved

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Last modified November 27 04:00 EST 2020. Contains 338677 sequences. (Running on oeis4.)