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Search: id:A088582
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| A088582 |
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Numbers of the form n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=4. |
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+0
1
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| 1, 5, 37, 229, 1253, 6373, 30949, 145637, 669925, 3029221, 13514981, 59652325, 260978917, 1133394149, 4891490533, 20997617893, 89717094629, 381774870757, 1618725452005, 6841405683941, 28831638239461, 121190614972645
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum of reciprocals = 1.232389931990837220821336083..
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FORMULA
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a(n)= (13+(3n-1)*4^(n+1))/9 = 9*a(n-1)-24*a(n-2)+16*a(n-3). G.f.: (1-4x+16x^2)/((1-x)(1-4x)^2). - R. J. Mathar, Jul 22 2009
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EXAMPLE
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4*4^4 + 3*4^3 + 2*4^2 + 4 + 1 = 1253.
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PROGRAM
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(PARI) trajpolyn(n1, k) = { s=0; for(x1=0, 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) }
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CROSSREFS
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Sequence in context: A144954 A146195 A095924 this_sequence A088583 A015548 A054417
Adjacent sequences: A088579 A088580 A088581 this_sequence A088583 A088584 A088585
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Nov 20 2003
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EXTENSIONS
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Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 22 2009
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