OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
FORMULA
a(n) = (n+3)*hypergeom([-n-2, n], [2], -1) = Sum_{s=1..n+3} binomial(n+3,s) * binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021
MAPLE
T:= proc(i, j) option remember;
if j=0 then 1
elif i=0 then 0
else add(add(T(h, m), m=0..j), h=0..i-1)
fi; end:
seq(T(n+3, n), n=0..20); # G. C. Greubel, Jan 23 2020
MATHEMATICA
T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h, 0, i-1}, {m, 0, j}]]]; Table[T[n+3, n], {n, 0, 20}] (* G. C. Greubel, Jan 23 2020 *)
PROG
(Sage)
@CachedFunction
def T(i, j):
if (j==0): return 1
elif (i==0): return 0
else: return sum(sum(T(h, m) for m in (0..j)) for h in (0..i-1))
[T(n+3, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved