|
|
A076726
|
|
a(n) = Sum_{k>=0} (k^n)/(2^k).
|
|
10
|
|
|
2, 2, 6, 26, 150, 1082, 9366, 94586, 1091670, 14174522, 204495126, 3245265146, 56183135190, 1053716696762, 21282685940886, 460566381955706, 10631309363962710, 260741534058271802, 6771069326513690646
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Ramesh L. Srigiriraju, Recurrences for A076726
|
|
FORMULA
|
a(n) = 2*A000670(n). - Philippe Deléham, Mar 06 2004
a(n) ~ n! / (log(2))^(n+1). - Vaclav Kotesovec, Nov 28 2013
|
|
EXAMPLE
|
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 + ...
|
|
MATHEMATICA
|
f[n_] := Sum[(k^n)/(2^k), {k, 0, Infinity}]; Table[ f[n], {n, 0, 18}]
a[n_] := (-1)^(n+1) PolyLog[-n, 2] (* Vladimir Reshetnikov, Jan 23 2011 *)
|
|
PROG
|
(PARI) a(n)=abs(polylog(-n, 2)) \\ Charles R Greathouse IV, Jul 15 2014
|
|
CROSSREFS
|
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
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Charles G. Waldman (cgw(AT)alum.mit.edu), Oct 27 2002
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v, Oct 29 2002
|
|
STATUS
|
approved
|
|
|
|