cp's OEIS Frontend

A377056 Antidiagonal-sums of the array A175804(n,k) = n-th term of k-th differences of partition numbers (A000041).

%I A377056 #6 Dec 15 2024 23:21:35
%S A377056 1,1,4,3,11,2,36,-27,142,-207,595,-1066,2497,-4878,10726,-22189,48383,
%T A377056 -103318,224296,-480761,1030299,-2186942,4626313,-9740648,20492711,
%U A377056 -43109372,90843475,-191769296,405528200,-858373221,1817311451,-3845483855,8129033837
%N A377056 Antidiagonal-sums of the array A175804(n,k) = n-th term of k-th differences of partition numbers (A000041).
%e A377056 Antidiagonal i + j = 3 of A175804 is (3, 1, 0, -1), so a(3) = 3.
%t A377056 nn=20;
%t A377056 t=Table[Differences[PartitionsP/@Range[0,2nn],k],{k,0,nn}];
%t A377056 Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]
%Y A377056 For primes we have A140119 or A376683, unsigned A376681 or A376684.
%Y A377056 These are the antidiagonal-sums of A175804.
%Y A377056 First column of the same array is A281425.
%Y A377056 For composites we have A377034, unsigned A377035.
%Y A377056 For squarefree numbers we have A377039, unsigned A377040.
%Y A377056 For nonsquarefree numbers we have A377049, unsigned A377048.
%Y A377056 For prime powers we have A377052, unsigned A377053.
%Y A377056 The unsigned version is A378621.
%Y A377056 The version for strict partitions is A378970 (row-sums of A378622), unsigned A378971.
%Y A377056 A000009 counts strict integer partitions, differences A087897, A378972.
%Y A377056 A000041 counts integer partitions, differences A002865, A053445.
%Y A377056 Cf. A008284, A047966, A075526, A116608, A225486, A293467, A325242, A325245, A325268, A377285.
%K A377056 sign
%O A377056 0,3
%A A377056 _Gus Wiseman_, Dec 12 2024