login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055815 a(n) = T(2*n+3,n), array T as in A055807. 7

%I

%S 1,15,80,432,2352,12896,71136,394400,2196128,12273648,68811184,

%T 386838480,2179890000,12309739968,69641542848,394643939904,

%U 2239678552640,12727572969680,72415319422992,412470467298032

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

%H G. C. Greubel, <a href="/A055815/b055815.txt">Table of n, a(n) for n = 0..250</a>

%F 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

%p T:= proc(i, j) option remember;

%p if j=0 then 1

%p elif i=0 then 0

%p else add(add(T(h,m), m=0..j), h=0..i-1)

%p fi; end:

%p seq(T(n+3, n), n=0..20); # _G. C. Greubel_, Jan 23 2020

%t 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 *)

%o (Sage)

%o @CachedFunction

%o def T(i, j):

%o if (j==0): return 1

%o elif (i==0): return 0

%o else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))

%o [T(n+3, n) for n in (0..20)] # _G. C. Greubel_, Jan 23 2020

%Y Cf. A050149. - _R. J. Mathar_, Oct 13 2008

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

%K nonn

%O 0,2

%A _Clark Kimberling_, May 28 2000

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 00:56 EDT 2021. Contains 343197 sequences. (Running on oeis4.)