|
|
A034177
|
|
a(n) is the n-th quartic factorial number divided by 4.
|
|
18
|
|
|
1, 8, 96, 1536, 30720, 737280, 20643840, 660602880, 23781703680, 951268147200, 41855798476800, 2009078326886400, 104472072998092800, 5850436087893196800, 351026165273591808000, 22465674577509875712000, 1527665871270671548416000, 109991942731488351485952000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
4*a(n) = (4*n)(!^4) = Product_{j=1..n} 4*j = 4^n * n!.
E.g.f.: (-1 + 1/(1-4*x))/4.
D-finite with recurrence: a(n) -4*n*a(n-1)=0. - R. J. Mathar, Feb 24 2020
Sum_{n>=1} 1/a(n) = 4*(exp(1/4)-1).
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*(1-exp(-1/4)). (End)
|
|
EXAMPLE
|
G.f. = x + 8*x^2 + 96*x^3 + 1536*x^4 + 30720*x^5 + 737820*x^6 + ...
|
|
MAPLE
|
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) [4^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 15 2019
(Sage) [4^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Aug 15 2019
(GAP) List([1..20], n-> 4^(n-1)*Factorial(n) ); # G. C. Greubel, Aug 15 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|