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A088578
a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=2.
2
1, 3, 11, 35, 99, 259, 643, 1539, 3587, 8195, 18435, 40963, 90115, 196611, 425987, 917507, 1966083, 4194307, 8912899, 18874371, 39845891, 83886083, 176160771, 369098755, 771751939, 1610612739, 3355443203, 6979321859, 14495514627, 30064771075, 62277025795
OFFSET
0,2
COMMENTS
For x=1 this is A000124.
Equals row sums of triangle A144332. Left border of A144332 = A000124. - Gary W. Adamson, Sep 18 2008
FORMULA
a(n) = (n-1) * 2^(n+1) + 3.
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). - Colin Barker, Apr 02 2012
G.f.: (1-2*x+4*x^2)/((1-x)*(1-2*x)^2). - Colin Barker, Apr 02 2012
EXAMPLE
Sum of reciprocals = 1.469480896985753544533086291..
MATHEMATICA
LinearRecurrence[{5, -8, 4}, {1, 3, 11}, 40] (* Harvey P. Dale, Dec 22 2013 *)
Table[(n - 1) 2^(n + 1) + 3, {n, 0, 30}] (* Vincenzo Librandi, Jun 14 2015 *)
PROG
(PARI) trajpolypn(n1, k) = { s=0; for(x1=1, n1, y1 = polypn2(k, x1); print1(y1", "); s+=1.0/y1; ); print(); print(s) } polypn2(n, p) = { x=n; y=1; for(m=1, p, y=y+m*x^m; ); return(y) }
(PARI) Vec((1-2*x+4*x^2)/((1-x)*(1-2*x)^2) + O(x^50)) \\ Colin Barker, Jun 13 2015
(Magma) I:=[1, 3, 11]; [n le 3 select I[n] else 5*Self(n-1)-8*Self(n-2)+4*Self(n-3): n in [1..35]]; // Vincenzo Librandi, Jun 14 2015
CROSSREFS
Cf. A000124.
Cf. A144332.
Sequence in context: A094308 A166046 A223626 * A320683 A027060 A171498
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Nov 20 2003
STATUS
approved