|
|
A181474
|
|
Sequence related to the Hankel transform of A105523(n+5).
|
|
1
|
|
|
1, 2, 10, 15, 42, 56, 120, 150, 275, 330, 546, 637, 980, 1120, 1632, 1836, 2565, 2850, 3850, 4235, 5566, 6072, 7800, 8450, 10647, 11466, 14210, 15225, 18600, 19840, 23936, 25432, 30345, 32130, 37962, 40071, 46930
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The Hankel transform of A105523(n+5) is (-1)^C(n+2,2)a(n+1).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1+x+4x^2+x^3+x^4)/((1-x)^5(1+x)^4);
a(n) = 2^n*(n+2)*(n+3)*Gamma(floor(n/2)+3)*Gamma(floor((n+1)/2)+1/2)/(12n!*sqrt(Pi)) (suggested by WolframAlpha).
a(n) = +a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9). a(n) = (n+3)*(n+2)*(2*n^2+2*(-1)^n*n+10*n+5*(-1)^n+11)/96. [R. J. Mathar, Oct 23 2010]
|
|
MATHEMATICA
|
CoefficientList[Series[(1 + x + 4 x^2 + x^3 + x^4)/((1 - x)^5 (1 + x)^4), {x, 0, 36}], x] (* Michael De Vlieger, Jul 25 2023 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|