A165792 -id:A165792 - cp's OEIS frontend

A165813 a(n) = n*(a(n-1)+3), a(0)=1.

1, 4, 14, 51, 216, 1095, 6588, 46137, 369120, 3322107, 33221100, 365432133, 4385185632, 57007413255, 798103785612, 11971556784225, 191544908547648, 3256263445310067, 58612742015581260, 1113642098296043997

Offset: 0

Philippe Deléham, Sep 28 2009

nonn

G. C. Greubel, Table of n, a(n) for n = 0..250

Cf. A000142, A033540, A165792.

FoldList[#1*#2 + 3 #2 &, 1, Range[19]] (* Robert G. Wilson v, Jul 07 2012 *)

a(n) = n! + 3*floor(e*n!) - 3. - Gary Detlefs, Jun 06 2010

A166677 a(n)= n*(a(n-1)+4), a(0)=1.

Original entry on oeis.org

1, 5, 18, 66, 280, 1420, 8544, 59836, 478720, 4308516, 43085200, 473937244, 5687246976, 73934210740, 1035078950416, 15526184256300, 248418948100864, 4223122117714756, 76016198118865680, 1444307764258447996

Offset: 0

Philippe Deléham, Oct 18 2009

G. C. Greubel, Table of n, a(n) for n = 0..200

Cf. A000142, A033540, A165792, A165813

f:= gfun:-rectoproc({a(n)=n*(a(n-1)+4),a(0)=1},a(n),remember):
map(f, [$0..30]); # Robert Israel, May 22 2016

FoldList[#1*#2 + 4 #2 &, 1, Range[19]] (* Robert G. Wilson v, Jul 07 2012 *)

a(n) = n!+4*floor(e*n!)-4, n>0. [Gary Detlefs, Jun 06 2010]
From Robert Israel, May 22 2016: (Start)
a(n) = n!*(1 + Sum_{k=0..n-1} 4/k!) = n! + 4 e n Gamma(n,1).
E.g.f.: (1+4*x*exp(x))/(1-x). (End)

cp's OEIS Frontend

A165813 a(n) = n*(a(n-1)+3), a(0)=1.

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