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A232845 a(0) = 0, a(1) = 1, and for n>=2, a(n) = (n-2)*a(n-1) - (n-1)*a(n-2). 2
0, 1, 0, -2, -4, -4, 4, 44, 236, 1300, 8276, 61484, 523804, 5024036, 53478980, 624890236, 7946278604, 109195935284, 1612048228276, 25439293045580, 427278358483196, 7609502950269124, 143217213477235364, 2840152418116021916, 59189357288576068780 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Robert Israel, Table of n, a(n) for n = 0..452

FORMULA

a(n) ~ (n-3)!. - Vaclav Kotesovec, Jan 20 2014

E.g.f.: (1-x)^2*exp(x-1)*(Ei(1)-Ei(1-x))/2 -(1-x)^2*exp(x) - x/2 + 1. - Robert Israel, Jan 08 2018

a(n) = (-1)^(n+1)*C(n-1, 1) where C(n, x) are the Charlier polynomials (with parameter a=1) as given in A137338. (Evaluation at x = -1 gives the left factorials A003422.) - Peter Luschny, Nov 28 2018

EXAMPLE

a(8) = 6*44 - 7*4 = 236.

MAPLE

f:= gfun:-rectoproc({a(n)=(n-2)*a(n-1)-(n-1)*a(n-2), a(0)=0, a(1)=1}, a(n), remember):

map(f, [$0..30]); # Robert Israel, Jan 08 2018

# Alternative:

C := proc(n, x) option remember; if n > 0 then (x-n)*C(n-1, x)-n*C(n-2, x)

elif n = 0 then 1 else 0 fi end: A232845 := n -> (-1)^(n+1)*C(n-1, 1):

seq(A232845(n), n=0..24); # Peter Luschny, Nov 28 2018

MATHEMATICA

Flatten[{0, RecurrenceTable[{(-1+n) a[-2+n]+(2-n) a[-1+n]+a[n]==0, a[1]==1, a[2]==0}, a, {n, 20}]}] (* Vaclav Kotesovec, Jan 20 2014 *)

CROSSREFS

Cf. A153229, A137338, A003422.

Sequence in context: A009145 A009292 A009622 * A269300 A182215 A036443

Adjacent sequences:  A232842 A232843 A232844 * A232846 A232847 A232848

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Nov 30 2013

STATUS

approved

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Last modified May 18 14:41 EDT 2022. Contains 353816 sequences. (Running on oeis4.)