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A056199 A simple recurrence. 3
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

Table of n, a(n) for n=1..22.

FORMULA

a(1)=0, a(2)=1, a(n) = n * a(n-1) - Sum_{k=1..n-2} a(k).

a(1)=0, n>1 a(n)=(1/3)*(-1+sum(k=0, n, k!)) - 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

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}]

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.

STATUS

approved

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Last modified November 23 19:08 EST 2017. Contains 295128 sequences.