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A055815 a(n) = T(2*n+3,n), array T as in A055807. 7
1, 15, 80, 432, 2352, 12896, 71136, 394400, 2196128, 12273648, 68811184, 386838480, 2179890000, 12309739968, 69641542848, 394643939904, 2239678552640, 12727572969680, 72415319422992, 412470467298032 (list; graph; refs; listen; history; text; internal format)
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

Cf. A050149. - R. J. Mathar, Oct 13 2008

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

Sequence in context: A123865 A024002 A050149 * A338414 A244855 A102360

Adjacent sequences:  A055812 A055813 A055814 * A055816 A055817 A055818

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 28 2000

STATUS

approved

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Last modified March 8 20:52 EST 2021. Contains 341953 sequences. (Running on oeis4.)