|
|
A330045
|
|
Expansion of e.g.f. exp(x) / (1 - x^4).
|
|
9
|
|
|
1, 1, 1, 1, 25, 121, 361, 841, 42001, 365905, 1819441, 6660721, 498971881, 6278929801, 43710250585, 218205219961, 21795091762081, 358652470233121, 3210080802962401, 20298322381652065, 2534333270094778681, 51516840824285500441, 563561785768079119561
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Sum_{k>=0} (4*k)! * x^(4*k) / (1 - x)^(4*k + 1).
a(0) = a(1) = a(2) = a(3) = 1; a(n) = n*(n - 1)*(n - 2)*(n - 3)*a(n - 4) + 1.
a(n) = Sum_{k=0..floor(n/4)} n! / (n - 4*k)!.
a(n) ~ n! * (2*cos(Pi*n/2 - 1) + exp(1) + (-1)^n*exp(-1))/4. - Vaclav Kotesovec, Apr 18 2020
|
|
MATHEMATICA
|
nmax = 22; CoefficientList[Series[Exp[x]/(1 - x^4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[n!/(n - 4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|