A378970 Antidiagonal-sums of the array A378622(n,k) = n-th term of k-th differences of strict partition numbers (A000009).

1, 1, 1, 5, -4, 18, -20, 47, -56, 110, -153, 309, -532, 1045, -1768, 2855, -3620, 2928, 2927, -20371, 62261, -148774, 314112, -613835, 1155936, -2175658, 4244218, -8753316, 19006746, -42471491, 95234915, -210395017, 453414314, -949507878, 1931940045

Offset: 0

Author

Gus Wiseman, Dec 14 2024

Keywords

• sign

Examples

			Antidiagonal 4 of A378622 is (2, 0, -1, -2, -3), so a(4) = -4.
		

Crossrefs

For primes we have A140119 or A376683, absolute value A376681 or A376684.

For composites we have A377034, absolute value A377035.

For squarefree numbers we have A377039, absolute value A377040.

For nonsquarefree numbers we have A377047, absolute value A377048.

For prime powers we have A377052, absolute value A377053.

For partition numbers we have A377056, absolute value A378621.

Row-sums of the triangular form of A378622. See also:

- A175804 is the version for partitions.

- A293467 gives the first column (up to sign).

- A377285 gives position of first zero in each row.

The unsigned version is A378971.

A000009 counts strict integer partitions, differences A087897, A378972.

A000041 counts integer partitions, differences A002865, A053445.

Cf. A008284, A047966, A098859, A116608, A225486, A325242, A325244.

Programs

Mathematica

nn=30;
t=Table[Take[Differences[PartitionsQ/@Range[0,2nn],k],nn],{k,0,nn}];
Total/@Table[t[[j,i-j+1]],{i,nn/2},{j,i}]