This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A132609 #15 Mar 05 2025 13:42:45 %S A132609 1,2,6,26,147,1026,8532,82394,906485,11194402,153347766,2307805402, %T A132609 37851581159,672037936898,12841521329896,262772642843802, %U A132609 5733086299727913,132853067341477538,3258726189638877610 %N A132609 Antidiagonal sum of table A072590(n,k) = n^(k-1)*k^(n-1) for n>=1. %C A132609 A072590(n,k) equals the number of spanning trees in complete bipartite graph K(n,k). %C A132609 Also the number of minimum connected dominating sets of the (n+1)-triangular honeycomb bishop graph. - _Eric W. Weisstein_, Jun 03 2024 and Mar 05 2025 %H A132609 Harvey P. Dale, <a href="/A132609/b132609.txt">Table of n, a(n) for n = 1..429</a> %H A132609 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>. %H A132609 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularHoneycombBishopGraph.html">Triangular Honeycomb Bishop Graph</a>. %F A132609 a(n) = Sum_{k=1..n} (n-k+1)^(k-1)*k^(n-k) for n>=1. %F A132609 a(n) ~ sqrt(2*Pi/3) * exp(1) * n^(n - 1/2) / 2^n. - _Vaclav Kotesovec_, Nov 22 2021 %t A132609 Table[Sum[(n - k + 1)^(k - 1) k^(n - k), {k, n}], {n, 30}] (* _Harvey P. Dale_, Jun 26 2021 *) %o A132609 (PARI) a(n)=sum(k=1,n,(n-k+1)^(k-1)*k^(n-k)) %Y A132609 Cf. A072590, A062817; A132608. %K A132609 nonn %O A132609 1,2 %A A132609 _Paul D. Hanna_, Aug 26 2007