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

0,5

Links

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

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A081130.

Sequence in context: A045652 A149430 A124463 * A005490 A174299 A351028

Adjacent sequences: A081194 A081195 A081196 * A081198 A081199 A081200

Keyword

easy,nonn

Author

Paul Barry, Mar 11 2003

Extensions

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

Status

approved