OFFSET
0,3
COMMENTS
n-m | a(n)-a(m) for all n,m.
LINKS
Robert Israel, Table of n, a(n) for n = 0..225
FORMULA
a(n) = A003470(2n-1) for n >= 1.
a(n) = n*hypergeom([1,n+1,1-n],[],-1).
a(n+3) = -a(n)+(4*n^2+6*n-1)*a(n+1)+(4*n^2+18*n+17)*a(n+2)+8*n+12.
D-finite with recurrence +(-2*n+5)*a(n) +(2*n-5)*(4*n^2-6*n+1)*a(n-1) -(2*n-1)*(4*n^2-18*n+19)*a(n-2) +(2*n-1)*a(n-3)=0. - R. J. Mathar, Jul 27 2022
MAPLE
f:= n -> add(mul(n-m, m=-k..k), k=0..n):
map(f, [$0..40]);
MATHEMATICA
Table[Sum[Product[n - j, {j, -m, m}], {m, 0, n}], {n, 0, 25}] (* G. C. Greubel, Dec 07 2016 *)
PROG
(PARI) a(n) = sum(m=0, n-1, prod(j=-m, m, n-j)); \\ Michel Marcus, Dec 07 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Dec 06 2016
STATUS
approved