A081197 Diagonal sums of A081130.

0, 0, 0, 1, 4, 13, 44, 162, 643, 2724, 12259, 58423, 293902, 1555743, 8640526, 50222288, 304792741, 1927313470, 12673784445, 86517541197, 612134881624, 4482215342305, 33919417267456, 264951302794510, 2133720505175351

Offset: 0

Author

Paul Barry, Mar 11 2003

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A081130.

Programs

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

Maple

A081197 := proc(n)
    add(k^(n-k-2)*binomial(n-k,2), k=1..n-2) ;
end proc: # R. J. Mathar, Feb 13 2015

Mathematica

Table[Sum[k^(n-k-2)*Binomial[n-k, 2], {k,n-2}], {n,0,30}] (* G. C. Greubel, May 15 2021 *)

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

Formula

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

a(n) = Sum_{k=0..n-1} (n-k)^(k-2)*binomial(k, 2). - G. C. Greubel, May 15 2021

Extensions

Terms corrected by G. C. Greubel, May 15 2021