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A056199 a(n) = n * a(n-1) - Sum_{k=1..n-2} a(k) with a(1) = 0 and a(2) = 1. 5
0, 1, 3, 11, 51, 291, 1971, 15411, 136371, 1345971, 14651571, 174318771, 2249992371, 31309422771, 467200878771, 7441464174771, 126003940206771, 2260128508782771, 42808495311726771, 853775831370606771, 17884089888607086771, 392550999147809646771 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..450

FORMULA

a(1)=0, a(n) = (1/3)*(-1 + Sum_{k=0..n} k!) for n > 1. - Benoit Cloitre, Nov 12 2005

a(n) = A007489(n)/3 for n >= 2. - Philippe Deléham, Feb 10 2007

G.f.: x*(W(0)/(2-2*x)/3 -1/3), where W(k) = 1 + 1/( 1 - x*(k+2)/( x*(k+2) + 1/W(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 20 2013

G.f.: 1/(3*(1-x)*Q(0)) - 1/3, m=+2, where Q(k) = 1 - 2*x*(2*k+1) - m*x^2*(k+1)*(2*k+1)/( 1 - 2*x*(2*k+2) - m*x^2*(k+1)*(2*k+3)/Q(k+1) ) ; (continued fraction). - Sergei N. Gladkovskii, Sep 24 2013

Given g.f. A(x) = x^2*F(x), then F(x) = (1-x)/(1 - 4*x + 4*x^2) * (1 + x^2*F'(x)). - Paul D. Hanna, Jan 16 2019

a(n) = (n+1)*a(n-1) - n*a(n-2) for n >= 4, a(n) = n*(n-1)/2 for n < 4. - Alois P. Heinz, Aug 11 2019

MAPLE

a:= proc(n) option remember; `if`(n<4, n*(n-1)/2,

      (n+1)*a(n-1) -n*a(n-2))

    end:

seq(a(n), n=1..23);  # Alois P. Heinz, Aug 11 2019

MATHEMATICA

a[1]=0; a[2]=1; a[n_Integer] := n*a[n-1]-Sum[a[k], {k, 1, n-2}]; Table[a[n], {n, 1, 22}]

Join[{0}, Table[Plus@@(Range[n]!) / 3, {n, 2, 25}]] (* Vincenzo Librandi, Jan 17 2019 *)

PROG

(MAGMA) [0] cat [&+[Factorial(i)/3: i in [1..n]]: n in [2..25]]; // Vincenzo Librandi, Jan 17 2019

CROSSREFS

Cf. A003422.

Sequence in context: A020043 A184819 A113712 * A230008 A007047 A182176

Adjacent sequences:  A056196 A056197 A056198 * A056200 A056201 A056202

KEYWORD

easy,nonn

AUTHOR

Robert G. Wilson v, Sep 26 1996

EXTENSIONS

New name using a formula from Robert G. Wilson v. - Paul D. Hanna, Jan 17 2019

STATUS

approved

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Last modified April 18 16:51 EDT 2021. Contains 343089 sequences. (Running on oeis4.)