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 A096401 #33 Jan 16 2022 11:09:28 %S A096401 1,0,0,0,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,8,8,10,11,13,14,17,18,21, %T A096401 23,26,28,32,35,39,43,48,53,59,65,72,80,88,97,107,118,129,142,155,171, %U A096401 186,204,222,244,265,290,315,345,374,409,443,484,524,571,618,673,727,790 %N A096401 Number of balanced partitions of n into distinct parts: least part is equal to number of parts. %H A096401 Seiichi Manyama, <a href="/A096401/b096401.txt">Table of n, a(n) for n = 1..1000</a> %F A096401 G.f.: Sum_{m>=1} (x^(m*(3*m-1)/2)-x^(m*(3*m+1)/2))/Product_{i=1..m} (1-x^i). %F A096401 a(n) = A025157(n) - A237979(n) = A237977(n) - A237976(n) for n > 0. - _Seiichi Manyama_, Jan 13 2022 %F A096401 a(n) ~ (1 - A263719) * A025157(n). - _Vaclav Kotesovec_, Jan 15 2022 %e A096401 a(14)=3 because we have 12+2, 7+4+3 and 6+5+3. %p A096401 G:=sum((x^(m*(3*m-1)/2)-x^(m*(3*m+1)/2))/product(1-x^i,i=1..m),m=1..20): Gser:=series(G,x=0,80): seq(coeff(Gser,x^n),n=1..78); # _Emeric Deutsch_, Mar 29 2005 %o A096401 (PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, x^(k*(3*k-1)/2)/prod(j=1, k-1, 1-x^j))) \\ _Seiichi Manyama_, Jan 15 2022 %Y A096401 Cf. A000009, A025157, A237976, A237977, A237979. %Y A096401 Cf. A006141, A047993, A339446. %K A096401 easy,nonn %O A096401 1,12 %A A096401 _Vladeta Jovovic_, Aug 06 2004 %E A096401 More terms from _Emeric Deutsch_, Mar 29 2005