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A140787
Expansion of 1 / ( (1+x)*(2*x+1)*(-1+2*x)^2 ).
1
1, 1, 7, 9, 39, 57, 199, 313, 967, 1593, 4551, 7737, 20935, 36409, 94663, 167481, 422343, 757305, 1864135, 3378745, 8155591, 14913081, 35418567, 65244729, 152859079, 283348537, 656175559, 1222872633, 2803659207, 5249404473
OFFSET
0,3
FORMULA
a(n) = 2^n*(n/3 + 11/18) + (-1)^n* (2^(n-1) - 1/9).
a(2n) - 2a(2n-1) = A002450(n+1).
a(n) + a(n+1) = A134353(n+1). - R. J. Mathar, Nov 10 2013
MATHEMATICA
max = 40; j[n_] := (2^n-(-1)^n)/3; jj = Table[{j[n], -j[n]}, {n, 0, max+2, 2}] // Flatten; a[0] = 1; a[n_] := a[n] = 2*a[n-1] + jj[[n+3]]; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Sep 30 2013 *)
PROG
(Magma) [2^n*(n/3+11/18) + (-1)^n* (2^(n-1)-1/9): n in [0..40]]; // Vincenzo Librandi, Aug 08 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jul 14 2008
EXTENSIONS
Better name from R. J. Mathar, Jul 02 2011
Edited by Ralf Stephan, Nov 10 2013
STATUS
approved