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A014288
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[ Sum k!/2, k=0..n ], or floor( A003422(n+1)/2 ).
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7
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0, 1, 2, 5, 17, 77, 437, 2957, 23117, 204557, 2018957, 21977357, 261478157, 3374988557, 46964134157, 700801318157, 11162196262157, 189005910310157, 3390192763174157, 64212742967590157, 1280663747055910157, 26826134832910630157, 588826498721714470157
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OFFSET
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0,3
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COMMENTS
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The first term a(0) would be a fraction if the floor( ... ) function would be omitted ; for n>=2, all terms from A003422 are even. - M. F. Hasler, Dec 16 2007
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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FORMULA
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a(0)=0, a(1)=1, a(2)=2, a(n)=(n+1)*a(n-1)-n*a(n-2). - Benoit Cloitre, Sep 07 2002
a(0) = 0, a(n) = (1/2)*Floor[1+1*Floor[1+2*Floor[1+....+(n-1)*Floor[1+n*Floor[1]]]....]. [From Joseph E. Cooper III (easonrevant(AT)gmail.com), Aug 19 2008]
G.f.: G(0)/(1-x)/2 -1/2, where G(k)= 1 + (2*k + 1)*x/( 1 - 2*x*(k+1)/(2*x*(k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 24 2013
G.f.: A(x)= ( Sum_{n>=0}*x^n*n!)/(2-2*x) - 1/2 = G(0)/(4*(1-x)) -1/2, where G(k)= 1 + 1/(1 - x/(x + 1/(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 02 2013
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MAPLE
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a:= proc(n) a(n):= `if`(n<3, n, (n+1)*a(n-1)-n*a(n-2)) end:
seq(a(n), n=0..25); # Alois P. Heinz, Feb 01 2013
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MATHEMATICA
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f[x_] := {Floor[1 + (n - x[[2]])*x[[1]]], x[[2]] + 1}
Nest[f, {1, 0}, n][[1]]/2 [From Joseph E. Cooper III (easonrevant(AT)gmail.com), Aug 19 2008]
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PROG
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(PARI) A014288(n)=sum(k=0, n, k!)>>1 \\ - M. F. Hasler, Dec 16 2007
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CROSSREFS
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Cf. A003422, A067078, A007489.
Sequence in context: A118100 A129591 A099825 * A199164 A184509 A020096
Adjacent sequences: A014285 A014286 A014287 * A014289 A014290 A014291
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Edited by M. F. Hasler, Dec 16 2007
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STATUS
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approved
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