A081197 - OEIS

%I #10 Sep 08 2022 08:45:09

%S 0,0,0,1,4,13,44,162,643,2724,12259,58423,293902,1555743,8640526,

%T 50222288,304792741,1927313470,12673784445,86517541197,612134881624,

%U 4482215342305,33919417267456,264951302794510,2133720505175351

%N Diagonal sums of A081130.

%H G. C. Greubel, <a href="/A081197/b081197.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = Sum_{k=1..n-2} k^(n-k-2)*binomial(n-k, 2).

%F a(n) = Sum_{k=0..n-1} (n-k)^(k-2)*binomial(k, 2). - _G. C. Greubel_, May 15 2021

%p A081197 := proc(n)

%p     add(k^(n-k-2)*binomial(n-k,2), k=1..n-2) ;

%p end proc: # _R. J. Mathar_, Feb 13 2015

%t Table[Sum[k^(n-k-2)*Binomial[n-k, 2], {k,n-2}], {n,0,30}] (* _G. C. Greubel_, May 15 2021 *)

%o (Magma) [n lt 3 select 0 else (&+[j^(n-j-2)*Binomial(n-j,2): j in [1..n-2]]): n in [0..30]]; // _G. C. Greubel_, May 15 2021

%o (Sage) [sum( (n-k)^(k-2)*binomial(k,2) for k in (0..n-1) ) for n in (0..30)] # _G. C. Greubel_, May 15 2021

%Y Cf. A081130.

%K easy,nonn

%O 0,5

%A _Paul Barry_, Mar 11 2003

%E Terms corrected by _G. C. Greubel_, May 15 2021