A377056 - OEIS

%I #6 Dec 15 2024 23:21:35

%S 1,1,4,3,11,2,36,-27,142,-207,595,-1066,2497,-4878,10726,-22189,48383,

%T -103318,224296,-480761,1030299,-2186942,4626313,-9740648,20492711,

%U -43109372,90843475,-191769296,405528200,-858373221,1817311451,-3845483855,8129033837

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

%e Antidiagonal i + j = 3 of A175804 is (3, 1, 0, -1), so a(3) = 3.

%t nn=20;

%t t=Table[Differences[PartitionsP/@Range[0,2nn],k],{k,0,nn}];

%t Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]

%Y For primes we have A140119 or A376683, unsigned A376681 or A376684.

%Y These are the antidiagonal-sums of A175804.

%Y First column of the same array is A281425.

%Y For composites we have A377034, unsigned A377035.

%Y For squarefree numbers we have A377039, unsigned A377040.

%Y For nonsquarefree numbers we have A377049, unsigned A377048.

%Y For prime powers we have A377052, unsigned A377053.

%Y The unsigned version is A378621.

%Y The version for strict partitions is A378970 (row-sums of A378622), unsigned A378971.

%Y A000009 counts strict integer partitions, differences A087897, A378972.

%Y A000041 counts integer partitions, differences A002865, A053445.

%Y Cf. A008284, A047966, A075526, A116608, A225486, A293467, A325242, A325245, A325268, A377285.

%K sign

%O 0,3

%A _Gus Wiseman_, Dec 12 2024