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.

A053421 Number of 5-multigraphs on n nodes.

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%I A053421 #16 Jul 10 2024 02:59:28
%S A053421 1,6,56,2451,533358,661452084,4364646955812,152397092027960154,
%T A053421 28427450083725134688228,28645398830642924774967347088,
%U A053421 157458251108667629202718200130101672,4760428376101385226312810920945121043818096
%N A053421 Number of 5-multigraphs on n nodes.
%D A053421 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.
%H A053421 Andrew Howroyd, <a href="/A053421/b053421.txt">Table of n, a(n) for n = 1..50</a>
%H A053421 Harald Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/html/book/hyl00_42.html">The cycle type of the induced action on 2-subsets</a>
%H A053421 Vladeta Jovovic, <a href="/A063843/a063843.rtf">Formulae for the number T(n,k) of n-multigraphs on k nodes</a>
%o A053421 (Python)
%o A053421 from itertools import combinations
%o A053421 from math import prod, gcd, factorial
%o A053421 from fractions import Fraction
%o A053421 from sympy.utilities.iterables import partitions
%o A053421 def A053421(n): return int(sum(Fraction(6**(sum(p[r]*p[s]*gcd(r,s) for r,s in combinations(p.keys(),2))+sum((q>>1)*r+(q*r*(r-1)>>1) for q, r in p.items())),prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n))) # _Chai Wah Wu_, Jul 09 2024
%Y A053421 Column k=5 of A063841.
%Y A053421 Cf. A000088, A004102, A053400.
%K A053421 easy,nonn
%O A053421 1,2
%A A053421 _Vladeta Jovovic_, Jan 11 2000
%E A053421 a(12) from _Andrew Howroyd_, Oct 22 2017