|
|
A330603
|
|
a(n) = Sum_{k>=0} (k - n)^n / 2^(k + 1).
|
|
2
|
|
|
1, 0, 3, -14, 155, -1834, 27867, -492246, 10068459, -232990178, 6025718963, -172182404734, 5387697769467, -183214963001082, 6728091949444491, -265348057242998822, 11185888456798395563, -501937946696294628946, 23886968118494957119011, -1201674025637823778926414
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The n-th term of the n-th inverse binomial transform of A000670.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n! * [x^n] exp(-n*x) / (2 - exp(x)).
a(n) = Sum_{k=0..n} binomial(n,k) * (-n)^(n - k) * A000670(k).
|
|
MATHEMATICA
|
Table[Sum[(k - n)^n/2^(k + 1), {k, 0, Infinity}], {n, 0, 19}]
Table[HurwitzLerchPhi[1/2, -n, -n]/2, {n, 0, 19}]
Table[n! SeriesCoefficient[Exp[-n x]/(2 - Exp[x]), {x, 0, n}], {n, 0, 19}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|