cp's OEIS Frontend

A307027 Number of (undirected) paths in the complete bipartite graph K_{m,n} (triangle read by rows with m = 1..n and n = 1..).

%I A307027 #8 Feb 16 2025 08:33:55
%S A307027 1,3,12,6,33,135,10,72,438,2224,15,135,1140,8850,55725,21,228,2511,
%T A307027 27480,265665,2006316,28,357,4893,70462,962010,11158203,98309827,36,
%U A307027 528,8700,156768,2818740,46176816,624859788,6291829440,45,747,14418,313434,7054875,152212365,2909139912
%N A307027 Number of (undirected) paths in the complete bipartite graph K_{m,n} (triangle read by rows with m = 1..n and n = 1..).
%H A307027 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>
%H A307027 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>
%F A307027 a(1, n) = binomial(n + 1, 2).
%F A307027 a(2, n) = n*(n^2 + 2).
%F A307027 a(3, n) = 3/2*n*(-3 + 11*n - 6*n^2 + 2*n^3).
%F A307027 a(4, n) = 2*n*(70 - 152*n + 123*n^2 - 42*n^3 + 6*n^4).
%F A307027 a(n, n) = A288035(n).
%e A307027 1;
%e A307027 3,12;
%e A307027 6,33,135;
%e A307027 10,72,438,2224;
%e A307027 15,135,1140,8850,55725;
%e A307027 21,228,2511,27480,265665,2006316;
%e A307027 28,357,4893,70462,962010,11158203,98309827;
%e A307027 36,528,8700,156768,2818740,46176816,624859788,6291829440;
%e A307027 45,747,14418,313434,7054875,152212365,2909139912,...;
%Y A307027 Cf. A288035 (K_{n,n} path count).
%K A307027 nonn,tabl,more
%O A307027 1,2
%A A307027 _Eric W. Weisstein_, Mar 20 2019