|
|
A305627
|
|
a(n) = (2^n / n!) * (2^1 - 1) * (2^2 - 1) * ... * (2^n - 1).
|
|
1
|
|
|
1, 2, 6, 28, 210, 2604, 54684, 1984248, 126495810, 14364301980, 2938936185108, 1093818612893832, 746531203300040340, 940744167112404680760, 2201744527114646554984440, 9619275055995416488956686064, 78799898849332452450472052650530
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
0 = +a(n)*(+a(n+1)*(+2*a(n+3)) +a(n+2)*(-6*a(n+2) +a(n+3))) +a(n+1)*(+a(n+1)*(+4*a(n+2) - 4*a(n+3)) +a(n+2)*(+4*a(n+2))) for all n in Z.
|
|
MATHEMATICA
|
a[ n_] := If[n < 0, 0, QPochhammer[2, 2, n] (-2)^n / n!];
|
|
PROG
|
(PARI) {a(n) = if( n<0, 0, prod(k=1, n, 2^k - 1) * 2^n / n!)};
(Magma) [1] cat [(&*[(2*k-1): k in [1..n]])*2^n/Factorial(n): n in [1..20]]; // G. C. Greubel, Jul 28 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|