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 A380412 #6 Feb 03 2025 19:55:42
%S A380412 1,0,0,1,-3,7,-14,25,-41,64,-100,165,-294,550,-1023,1795,-2823,3658,
%T A380412 -2882,-2873,20435,-62185,148863,-314008,613957,-1155794,2175823,
%U A380412 -4244026,8753538,-19006490,42471787,-95234575,210395407,-453413866,949508390,-1931939460
%N A380412 First term of the n-th differences of the strict partition numbers. Inverse zero-based binomial transform of A000009.
%C A380412 Up to sign, same as A293467.
%F A380412 a(n) = Sum_{k=0..n} (-1)^(n-k) binomial(n,k) A000041(k).
%t A380412 nn=10;Table[First[Differences[PartitionsQ/@Range[0,nn],n]],{n,0,nn}]
%Y A380412 The version for non-strict partitions is A281425, row n=0 of A175804.
%Y A380412 Column n=0 of A378622.
%Y A380412 A000009 counts strict integer partitions, differences A087897, A378972.
%Y A380412 A266232 gives zero-based binomial transform of A000009, differences A129519.
%Y A380412 Cf. A000041, A007442, A008284, A218482, A293467, A320590, A320591, A377285, A378970.
%K A380412 sign
%O A380412 0,5
%A A380412 _Gus Wiseman_, Feb 03 2025