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A076726
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a(n) = Sum_{k>=0} k^n/2^k.
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10
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2, 2, 6, 26, 150, 1082, 9366, 94586, 1091670, 14174522, 204495126, 3245265146, 56183135190, 1053716696762, 21282685940886, 460566381955706, 10631309363962710, 260741534058271802, 6771069326513690646
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listen;
history;
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internal format)
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OFFSET
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0,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Ramesh L. Srigiriraju, Recurrences for A076726
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FORMULA
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a(n) = 2*A000670(n). - Philippe Deléham, Mar 06 2004
a(n) ~ n! / (log(2))^(n+1). - Vaclav Kotesovec, Nov 28 2013
From Jianing Song, May 04 2022: (Start)
a(0) = 2, a(n) = Sum_{k=0..n-1} binomial(n,k)*a(k) for n >= 1.
G.f.: Sum_{k>=0} 1/(2^k*(1-k*x)).
E.g.f.: 1/(1-exp(x)/2). (End)
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EXAMPLE
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a(0) = 2 because 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 2; a(1) = 2 because 0 + 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + ... = 2.
G.f. = 2 + 2*x + 6*x^2 + 26*x^3 + 150*x^4 + 1082*x^5 + 9366*x^6 + 94586*x^7 + ...
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MATHEMATICA
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a[n_] := Sum[(k^n)/(2^k), {k, 0, Infinity}]; Table[ a[n], {n, 0, 18}]
a[n_] := (-1)^(n+1) PolyLog[-n, 2] (* Vladimir Reshetnikov, Jan 23 2011 *)
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PROG
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(PARI) a(n)=abs(polylog(-n, 2)) \\ Charles R Greathouse IV, Jul 15 2014
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CROSSREFS
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Same as A000629 except for a(0).
A000629, A000670, A002050, A052856, A076726 are all more-or-less the same sequence. - N. J. A. Sloane, Jul 04 2012
Sequence in context: A052660 A135407 A292831 * A032272 A214446 A179320
Adjacent sequences: A076723 A076724 A076725 * A076727 A076728 A076729
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KEYWORD
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nonn
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AUTHOR
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Charles G. Waldman (cgw(AT)alum.mit.edu), Oct 27 2002
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EXTENSIONS
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More terms from Robert G. Wilson v, Oct 29 2002
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STATUS
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approved
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