|
|
A094856
|
|
E.g.f.: exp(4x)/(1-4x)^(1/4).
|
|
6
|
|
|
1, 5, 29, 217, 2297, 34349, 674965, 16276481, 461527793, 14993138773, 548258687501, 22272738733865, 994870668959209, 48451779617935997, 2554818339078836357, 144990720049391354449, 8811240401831517313505, 570857963393730507892901, 39275973938444154366908413
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k = 0..n} A046716(n, k)*4^k.
a(n) ~ n^(n-1/4)*4^n*Gamma(3/4)/(exp(n-1)*sqrt(Pi)). - Vaclav Kotesovec, Oct 03 2012
Conjectured to be D-finite with recurrence: a(n) +(-4*n-1)*a(n-1) +16*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 15 2019
|
|
MATHEMATICA
|
Table[n!*SeriesCoefficient[E^(4x)/(1-4x)^(1/4), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 03 2012 *)
With[{nn=20}, CoefficientList[Series[Exp[4x]/(1-4x)^(1/4), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Mar 29 2013 *)
|
|
PROG
|
(PARI) x='x+O('x^66); Vec(serlaplace(exp(4*x)/(1-4*x)^(1/4))) \\ Joerg Arndt, May 11 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|