|
|
A076051
|
|
Sum of product of odd numbers <= n and the product of even numbers <= n.
|
|
2
|
|
|
2, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635, 4370620275, 17465201775, 95498916975, 397983749625, 2278224696825, 9867844134225, 58917607974225
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = o(n)+ e(n) where; o(n)=the product of odd numbers from 1 to n e(n)=the product of even numbers from 2 to n.
From Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002: (Start)
a(1)=2, a(2)=3, a(3)=5, a(n) = (n-1)*a(n-2) + (n-2)!! for n >= 4.
E.g.f.: 1 + x + (1+x+x^2)*(exp(x^2/2)*(1+sqrt(Pi/2)*erf(x/sqrt(2)))), where erf denotes the error function. (End)
|
|
MATHEMATICA
|
With[{nn = 25}, CoefficientList[Series[1 + x + (1 + x + x^2) *(Exp[x^2/2] *(1 + Sqrt[Pi/2]*Erf[x/Sqrt[2]])), {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, May 25 2017 *)
|
|
PROG
|
(PARI) for(n=1, 50, print1(2^(floor(n/2))*(floor(n/2))! + n!/(2^(floor(n/2))*(floor(n/2))!), ", ")) \\ G. C. Greubel, May 23 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Emrehan Halici (emrehan(AT)halici.com.tr), Oct 30 2002
|
|
EXTENSIONS
|
More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
|
|
STATUS
|
approved
|
|
|
|