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A286032 a(n) = a(n-1) - n*a(n-2); a(0) = a(1) = 1. 1
1, 1, -1, -4, 0, 20, 20, -120, -280, 800, 3600, -5200, -48400, 19200, 696800, 408800, -10740000, -17689600, 175630400, 511732800, -3000875200, -13747264000, 52271990400, 368459062400, -886068707200, -10097545267200, 12940241120000, 285573963334400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..500

FORMULA

a(n) = n! [x^n] (1 - sqrt(Pi / 2) * exp(-((x - 1)^2) / 2) * (x - 1) * (erfi((x - 1) / sqrt(2)) + erfi(1 / sqrt(2)))).

Generating function satisfies x^3*A'(x) + (2*x^2-x+1)*A(x) = 1.

MAPLE

a := proc(n) option remember;

if n <= 1 then 1 else a(n-1) - n*a(n-2) fi end:

seq(a(n), n = 0..27);

a_list := proc(len) 1 - sqrt(Pi/2)*exp(-((x-1)^2)/2)*(x-1)*

(erfi((x-1)/sqrt(2)) + erfi(1/sqrt(2))); series(%, x, len+2):

seq(n!*simplify(coeff(%, x, n)), n=0..len-1) end: a_list(27);

MATHEMATICA

l={1, 1}; Do[AppendTo[l, l[[-1]] - n*l[[-2]]], {n, 2, 30}]; l (* Indranil Ghosh, May 01 2017 *)

PROG

(Python)

l=[1, 1]

a=b=1

i=2

while i<=30:

    l+=[b - i*a, ]

    b=l[-1]

    a=l[-2]

    i+=1

print l # Indranil Ghosh, May 01 2017

CROSSREFS

Row sums of A137286.

Sequence in context: A283012 A284136 A284178 * A199933 A078630 A178671

Adjacent sequences:  A286029 A286030 A286031 * A286033 A286034 A286035

KEYWORD

sign

AUTHOR

Peter Luschny, May 01 2017

STATUS

approved

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Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)