A273528 Triangle T(n,m) (n >= 1, 0 <= m < n) giving coefficients of (n-1)! P_n, where P_n is the polynomial formula for row n of A213086.

1, 0, 1, 0, 1, 1, 0, 1, 3, 2, 0, 2, 9, 10, 3, 0, 2, 25, 50, 35, 8, 0, -12, 86, 270, 260, 102, 14, 0, -120, 140, 1344, 2030, 1260, 350, 36, 0, -1248, -1016, 7336, 15862, 13048, 5236, 1024, 78, 0, -9216, -22464, 28528, 124488, 139776, 76104, 22152, 3312, 200, 0, -90720, -322344, 1860, 1036990, 1514205, 1018563, 379890, 80760, 9165, 431

Offset

1,9

Links

Table of n, a(n) for n=1..66.

Formula

The first formulas (stripped of factorials) :

1,

k,

k + k^2,

k + 3 k^2 + 2 k^3,

2 k + 9 k^2 + 10 k^3 + 3 k^4,

2 k + 25 k^2 + 50 k^3 + 35 k^4 + 8 k^5,

-12 k + 86 k^2 + 270 k^3 + 260 k^4 + 102 k^5 + 14 k^6,

-120 k + 140 k^2 + 1344 k^3 + 2030 k^4 + 1260 k^5 + 350 k^6 + 36 k^7,

...

Example

Row T(5) = {0, 2, 9, 10, 3}, so P_5(k) = (1/4!)(2k + 9k^2 + 10k^3 + 3k^4), which gives 1, 7, 25, 65, 140, 266, ..., that is A001296 (row 5 of A213086), for k >=1.
Triangle begins:
{1},
{0, 1},
{0, 1, 1},
{0, 1, 3, 2},
{0, 2, 9, 10, 3},
{0, 2, 25, 50, 35, 8},
{0, -12, 86, 270, 260, 102, 14},
...

Crossrefs

Cf. A213086, A213074.

Sequence in context: A379542 A373088 A075115 * A085080 A376984 A260308

Adjacent sequences: A273525 A273526 A273527 * A273529 A273530 A273531

Keyword

sign,tabl

Author

Jean-François Alcover, May 24 2016

Status

approved