A187566 - OEIS

A187566

Let A be the infinite lower triangular Toplitz matrix with Sigma(n) in every column; and B the diagonalized, signed variant of A002040 with the rest zeros. Sequence gives the triangle in the lower half of A*B read by rows.

1, 3, -2, 4, -6, 4, 7, -8, 12, -8, 6, -14, 16, -24, 21, 12, -12, 28, -32, 63, -52, 8, -24, 24, -56, 84, -156, 131, 15, -16, 48, -48, 147, -208, 393, -316, 13, -30, 32, -96, 126, -364, 524, -948, 765, 18, -26, 60, -64, 252, -312, 917, -1264, 2295, -1846

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OFFSET

0,2

COMMENTS

Row sums = A000041, left border = A000203, main diagonal = A002040 (signed)

Equivalent to the statement that Sigma(n) convolved with A002040(signed +-+-+-...) = the partition numbers; such that (1 + 3x + 4x^2 +7x^3 + ...)*(1 -2x + 4x^2 - 8x^3 + ...) = (1 + x + 2x^2 + 3x^3 + 5x^4 + 7x^5 + ...).

A002040 = (1, 2, 4, 8, 21, 52, 131, 316, 765,...)

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

First few rows of the triangle =

3, -2

4, -6, 4

7, -8, 12, -8

6, -14, 16, -24, 21

12, -12, 28, -32, 63, -52

8, -24, 24, -56, 84, -156, 131

15, -16, 48, -48, 147, -208, 393, -316