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

1, 1, 4, 3, 11, 2, 36, -27, 142, -207, 595, -1066, 2497, -4878, 10726, -22189, 48383, -103318, 224296, -480761, 1030299, -2186942, 4626313, -9740648, 20492711, -43109372, 90843475, -191769296, 405528200, -858373221, 1817311451, -3845483855, 8129033837

Offset: 0

Author

Gus Wiseman, Dec 12 2024

Keywords

• sign

Examples

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

Crossrefs

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

These are the antidiagonal-sums of A175804.

First column of the same array is A281425.

For composites we have A377034, unsigned A377035.

For squarefree numbers we have A377039, unsigned A377040.

For nonsquarefree numbers we have A377049, unsigned A377048.

For prime powers we have A377052, unsigned A377053.

The unsigned version is A378621.

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

A000009 counts strict integer partitions, differences A087897, A378972.

A000041 counts integer partitions, differences A002865, A053445.

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

Programs

Mathematica

nn=20;
t=Table[Differences[PartitionsP/@Range[0,2nn],k],{k,0,nn}];
Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]