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 A304961 #23 Aug 22 2020 18:50:07
%S A304961 1,1,2,6,12,32,72,176,384,960,2112,4992,11264,26112,58368,136192,
%T A304961 301056,688128,1548288,3489792,7766016,17596416,38993920,87293952,
%U A304961 194248704,432537600,957349888,2132803584,4699717632,10406068224,23001563136,50683969536,111434268672,245819768832
%N A304961 Expansion of Product_{k>=1} (1 + 2^(k-1)*x^k).
%C A304961 Number of compositions of partitions of n into distinct parts. a(3) = 6: 3, 21, 12, 111, 2|1, 11|1. - _Alois P. Heinz_, Sep 16 2019
%C A304961 Also the number of ways to split a composition of n into contiguous subsequences with strictly decreasing sums. - _Gus Wiseman_, Jul 13 2020
%C A304961 This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1, g(n) = (-1) * 2^(n-1). - _Seiichi Manyama_, Aug 22 2020
%H A304961 Seiichi Manyama, <a href="/A304961/b304961.txt">Table of n, a(n) for n = 0..1000</a>
%H A304961 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A304961 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A304961 G.f.: Product_{k>=1} (1 + A011782(k)*x^k).
%F A304961 a(n) ~ 2^n * exp(2*sqrt(-polylog(2, -1/2)*n)) * (-polylog(2, -1/2))^(1/4) / (sqrt(6*Pi) * n^(3/4)). - _Vaclav Kotesovec_, Sep 19 2019
%e A304961 From _Gus Wiseman_, Jul 13 2020: (Start)
%e A304961 The a(0) = 1 through a(4) = 12 splittings:
%e A304961 () (1) (2) (3) (4)
%e A304961 (1,1) (1,2) (1,3)
%e A304961 (2,1) (2,2)
%e A304961 (1,1,1) (3,1)
%e A304961 (2),(1) (1,1,2)
%e A304961 (1,1),(1) (1,2,1)
%e A304961 (2,1,1)
%e A304961 (3),(1)
%e A304961 (1,1,1,1)
%e A304961 (1,2),(1)
%e A304961 (2,1),(1)
%e A304961 (1,1,1),(1)
%e A304961 (End)
%t A304961 nmax = 33; CoefficientList[Series[Product[(1 + 2^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%o A304961 (PARI) N=40; x='x+O('x^N); Vec(prod(k=1, N, 1+2^(k-1)*x^k)) \\ _Seiichi Manyama_, Aug 22 2020
%Y A304961 Cf. A000009, A011782, A022629, A098407, A102866, A266964, A271619, A279785.
%Y A304961 The non-strict version is A075900.
%Y A304961 Starting with a reversed partition gives A323583.
%Y A304961 Starting with a partition gives A336134.
%Y A304961 Partitions of partitions are A001970.
%Y A304961 Splittings with equal sums are A074854.
%Y A304961 Splittings of compositions are A133494.
%Y A304961 Splittings with distinct sums are A336127.
%Y A304961 Cf. A006951, A063834, A316245, A317715, A319794, A323582, A336135, A336136.
%K A304961 nonn
%O A304961 0,3
%A A304961 _Ilya Gutkovskiy_, May 22 2018