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.

A053420 Number of 4-multigraphs on n nodes.

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%I A053420 #16 Jul 10 2024 02:59:20
%S A053420 1,5,35,900,90005,43571400,95277592625,925609100039625,
%T A053420 40119721052610123750,7833164300852979350336250,
%U A053420 6953552738579427778531249187500,28293472829338822230349054996265275000,531350037528849507720092485196308155336875000
%N A053420 Number of 4-multigraphs on n nodes.
%D A053420 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.
%H A053420 Andrew Howroyd, <a href="/A053420/b053420.txt">Table of n, a(n) for n = 1..50</a>
%H A053420 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 A053420 Vladeta Jovovic, <a href="/A063843/a063843.rtf">Formulae for the number T(n,k) of n-multigraphs on k nodes</a>
%o A053420 (Python)
%o A053420 from itertools import combinations
%o A053420 from math import prod, gcd, factorial
%o A053420 from fractions import Fraction
%o A053420 from sympy.utilities.iterables import partitions
%o A053420 def A053420(n): return int(sum(Fraction(5**(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 A053420 Column k=4 of A063841.
%Y A053420 Cf. A000088, A004102, A053400.
%K A053420 easy,nonn
%O A053420 1,2
%A A053420 _Vladeta Jovovic_, Jan 11 2000
%E A053420 Terms a(12) and beyond from _Andrew Howroyd_, Oct 22 2017