OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..449
FORMULA
a(n) = 1 + Sum_{k=2..n} (floor((k + 1)/2)! * n!)/((n - floor(k/2))!). - G. C. Greubel, Oct 26 2017
a(n) ~ n!. - Vaclav Kotesovec, Oct 09 2020
EXAMPLE
a(0) = a(1) = 1;
a(2) = 1 + 1*2 = 3;
a(3) = 1 + 1*3 + 1*3*2 = 10;
a(4) = 1 + 1*4 + 1*4*2 + 1*4*2*3 = 37;
a(5) = 1 + 1*5 + 1*5*2 + 1*5*2*4 + 1*5*2*4*3 = 176; ...
MATHEMATICA
Join[{1}, Table[Sum[(Floor[(k + 1)/2]! * n!)/((n - Floor[k/2])!), {k, 1, n}], {n, 1, 50}]] (* G. C. Greubel, Oct 26 2017 *)
PROG
(PARI) {a(n)=if(n==0, 1, sum(k=1, n, prod(j=1, k, ((j+1)\2)*(j%2)+(n+1-(j\2))*((j-1)%2))))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 03 2006
STATUS
approved