A055815 a(n) = T(2*n+3,n), array T as in A055807.

1, 15, 80, 432, 2352, 12896, 71136, 394400, 2196128, 12273648, 68811184, 386838480, 2179890000, 12309739968, 69641542848, 394643939904, 2239678552640, 12727572969680, 72415319422992, 412470467298032

Offset: 0

Author

Clark Kimberling, May 28 2000

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Apart from the offset the same as A050149. - R. J. Mathar, Oct 13 2008

Cf. A055807, A055809, A055810, A055811, A055816, A055817.

Programs

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 *)

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

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