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.
%I A376821 #13 Oct 06 2024 13:10:11 %S A376821 0,0,0,0,0,0,0,1,1,0,1,0,0,3,3,6,7,8,4,6,7,12,17,23,23,31,38,36,70,71, %T A376821 101,127,118,145,191,209,261,309,396,462,512,652,769,878,1097,1320, %U A376821 1563,1827,2098,2533,2932,3475,4185,4756,5726,6614,7686,9189,10825 %N A376821 Number of irreducible pairs of partitions of n. %C A376821 A pair of partitions of n is irreducible if the two partitions yield the same multinomial coefficient but have no parts in common. The partitions in the pair are required to be distinct, otherwise a(0) would be 1. %H A376821 George E. Andrews, Arnold Knopfmacher, and Burkhard Zimmermann, <a href="https://doi.org/10.1016/j.jnt.2005.08.012">On the number of distinct multinomial coefficients</a>, Journal of Number Theory 118 (2006), 15-30; <a href="https://arxiv.org/abs/math/0509470">arXiv preprint</a>, arXiv:math/0509470 [math.CO], 2005. (See Section 7.) %e A376821 n | irreducible pairs of partitions of n %e A376821 ---+------------------------------------- %e A376821 7 | (1,1,1,4), (2,2,3) %e A376821 8 | (1,1,6), (3,5) %e A376821 10 | (1,4,5), (2,2,6) %e A376821 13 | (1,1,1,10), (6,7) %e A376821 | (1,1,3,8), (2,4,7) %e A376821 | (1,1,1,1,1,8), (2,2,2,7) %e A376821 14 | (1,2,2,9), (3,3,8) %e A376821 | (1,1,1,2,9), (3,4,7) %e A376821 | (1,1,1,1,1,1,4,4), (2,2,2,2,3,3) %Y A376821 Cf. A070289, A260669, A325306, A376661. %K A376821 nonn %O A376821 0,14 %A A376821 _Pontus von Brömssen_, Oct 05 2024