A055817 a(n) = T(2n+5,n), array T as in A055807.

1, 63, 448, 2816, 16896, 99200, 575872, 3322112, 19096064, 109541824, 627653440, 3594256896, 20577979392, 117814911744, 674630384384, 3864033226240, 22138650598400, 126885674577728, 727501822004416, 4172725286118656

Offset: 0

Author

Clark Kimberling, May 28 2000

Keywords

• nonn

Links

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

Crossrefs

Cf. A055807, A055809, A055810, A055811, A055815, A055816.

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+5, 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+5, 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+5, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

Formula

a(n) = (n+5)*hypergeom([-n-4, n], [2], -1) = Sum_{s=1..n+5} binomial(n+5,s) * binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021