cp's OEIS Frontend

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.

A055540 Total number of leaves (nodes of vertex degree 1) in all graphs of n nodes.

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%I A055540 #17 Feb 16 2025 08:32:43
%S A055540 0,2,4,14,38,153,766,6259,88064,2324157,116563882,11060411527,
%T A055540 1968703079886,654492092481733,406111248305672980,
%U A055540 471005105043787823717,1023566652048387537072658,4179937690541808658135640875,32172436158252943170541450460638
%N A055540 Total number of leaves (nodes of vertex degree 1) in all graphs of n nodes.
%H A055540 Andrew Howroyd, <a href="/A055540/b055540.txt">Table of n, a(n) for n = 1..50</a>
%H A055540 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TreeLeaf.html">Tree Leaf</a>
%F A055540 a(n) = Sum_{k=1..n} k*A327371(n, k). - _Andrew Howroyd_, Sep 04 2019
%o A055540 (PARI) \\ See A327371 for G.
%o A055540 seq(n)=Vec(subst(deriv(G(n), y), y, 1), -n) \\ _Andrew Howroyd_, Jan 22 2021
%Y A055540 Cf. A003227, A003228, A055541, A327371.
%K A055540 nonn
%O A055540 1,2
%A A055540 _Eric W. Weisstein_
%E A055540 a(8) and a(9) from _Eric W. Weisstein_, Jun 02 2004
%E A055540 a(10) from _Andrew Howroyd_, Sep 04 2019
%E A055540 Terms a(11) and beyond from _Andrew Howroyd_, Jan 22 2021