login
Square pyramid giving coefficients of Carlo Wood's polynomials, read by successive slices, each slice being read row by row.
1

%I #26 Jul 29 2022 16:53:14

%S 1,1,1,1,3,1,3,2,2,9,7,1,6,11,1,6,11,6,3,22,45,26,3,26,69,46,1,10,35,

%T 50,1,10,35,50,24,4,45,170,255,126,6,75,320,525,274,4,55,270,545,326,

%U 1,15,85,225,274,1,15,85,225,274,120,5,81,485,1335,1670,744,10

%N Square pyramid giving coefficients of Carlo Wood's polynomials, read by successive slices, each slice being read row by row.

%C There is no standard method for converting a pyramid of numbers to a sequence. This seems as good a solution as any.

%C See the link for further information and more terms.

%C The first row of each slice seems to coincide with the first row of each slice of A335442. That row from the n-th slice seems to be the coefficients of the polynomial (x+1) * ... * (x+n-1), i.e., the reversed row n-1 of A130534. - _Andrey Zabolotskiy_, Jun 26 2022

%H N. J. A. Sloane, <a href="/A126671/a126671.txt">Notes on Carlo Wood's Polynomials</a>

%e Slice 1:

%e 1

%e Slice 2:

%e 1 1

%e 1 3

%e Slice 3:

%e 1 3 2

%e 2 9 7

%e 1 6 11

%e Slice 4:

%e 1 6 11 6

%e 3 22 45 26

%e 3 26 69 46

%e 1 10 35 50

%e Note that in Part 4 of the linked file, the order of the rows is reversed, while in its Part 1 the order of both rows and columns is reversed.

%Y Cf. A126671, A130534, A335442.

%K nonn,tabf

%O 1,5

%A _N. J. A. Sloane_, Feb 14 2007

%E The sole term 1 of slice 1 inserted by _Andrey Zabolotskiy_, Jun 26 2022