(Translated by https://www.hiragana.jp/)
# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a053420 Showing 1-1 of 1 %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, Table of n, a(n) for n = 1..50 %H A053420 Harald Fripertinger, The cycle type of the induced action on 2-subsets %H A053420 Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE