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 A359175 #21 Mar 25 2024 10:43:32 %S A359175 0,9,48,200,780,2989,11424,43740,167940,646624,2496120,9657674, %T A359175 37442132,145422645,565722688,2203961396,8597496564,33578000572, %U A359175 131282408360,513791607378,2012616400036,7890371113904,30957699535728 %N A359175 a(n) = binomial(2*n-2,n) - 2*(n-1). %C A359175 a(n) is the number of ways to place n indistinguishable balls into n-1 distinguishable boxes with at least one box remaining empty and not all balls placed in one box. %F A359175 a(n) = A001791(n-1) - 2*(n-1), n > 2. %F A359175 G.f.: (x^4 - 2*x^3 - 2*x^2 + 2*x - 1)/(1 - x)^2 + 4*x^2/(sqrt(1 - 4*x)*(sqrt(1 - 4*x) - 1)^2). - _Stefano Spezia_, Dec 28 2022 %F A359175 D-finite with recurrence n*a(n) +7*(-n+1)*a(n-1) +2*(7*n-16)*a(n-2) +4*(-2*n+7)*a(n-3) +12*(n-5)=0. - _R. J. Mathar_, Jan 25 2023 %e A359175 For n=4, the 9 distributions are: %e A359175 |ooo|o| | %e A359175 |ooo| |o| %e A359175 |o|ooo| | %e A359175 | |ooo|o| %e A359175 |o| |ooo| %e A359175 | |o|ooo| %e A359175 |oo|oo| | %e A359175 |oo| |oo| %e A359175 | |oo|oo|. %Y A359175 Cf. A001791, A350653. %K A359175 nonn %O A359175 3,2 %A A359175 _Enrique Navarrete_, Dec 27 2022