A174740 - OEIS

A174740

Triangle read by rows, A027293 * an infinite lower triangular matrix with A147843 as the diagonal and the rest zeros.

1, 1, 2, 2, 2, 0, 3, 4, 0, 0, 5, 6, 0, 0, -5, 7, 10, 0, 0, -5, 0, 11, 14, 0, 0, -10, 0, -7, 15, 22, 0, 0, -15, 0, -7, 0, 22, 30, 0, 0, -25, 0, -14, 0, 0, 30, 44, 0, 0, -35, 0, -21, 0, 0, 0, 42, 60, 0, 0, -55, 0, -35, 0, 0, 0, 0, 56, 84, 0, 0, -75, 0, -49, 0, 0, 0, 0, 12

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OFFSET

1,3

COMMENTS

Left border = the partition numbers, A000041; right border = A147843 starting (1, 2, 0, ...).

Row sums apparently give A000203. Check: Sum of row 6 terms = [7, 5, 3, 2, 1, 1] dot [1, 2, 0, 0, -5, 0] = [7 + 10 + 0 + 0 -5 + 0] = 12 = A000203(6).

LINKS

Table of n, a(n) for n=1..78.

FORMULA

Equals triangle A027293 * a lower triangular matrix with A147843 (deleting the first zero) as the right border and the rest zeros.

T(n,k) = A147843(k) * A027293(n,k). - Joerg Arndt, Dec 29 2022

EXAMPLE

First few rows of the triangle:

1, 2;

2, 2, 0;

3, 4, 0, 0;

5, 6, 0, 0, -5;

7, 10, 0, 0, -5, 0;

11, 14, 0, 0, -10, 0, -7;

15, 22, 0, 0, -15, 0, -7, 0;

22, 30, 0, 0, -25, 0, -14, 0, 0;

30, 44, 0, 0, -35, 0, -21, 0, 0, 0;

42, 60, 0, 0, -55, 0, -35, 0, 0, 0, 0;

56, 84, 6, 0, -75, 0, -49, 0, 0, 0, 0, 12;

...

CROSSREFS

Cf. A027293, A147843, A000041, A000203.

Sequence in context: A071441 A134577 A071442 * A124759 A071295 A296062

Adjacent sequences: A174737 A174738 A174739 * A174741 A174742 A174743

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Mar 28 2010

EXTENSIONS

Terms corrected by Gary W. Adamson, Dec 27 2022

STATUS

approved