A055816 a(n) = T(2*n+4,n), array T as in A055807.

1, 31, 192, 1120, 6400, 36288, 205184, 1159488, 6554880, 37088480, 210075712, 1191254688, 6762782208, 38434677120, 218663320320, 1245254943872, 7098135387648, 40495661150112, 231220652273600, 1321222104326880

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, 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+4, 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+4, 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+4, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

Formula

a(n) = (n+4)*hypergeom([-n -3, n], [2], -1) = Sum_{s=1..n+4} binomial(n+4,s)*binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021