login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Column sums of a Gaussian polynomial-shaped array. Row sums generate the Eulerian array A008292.
1

%I #4 Sep 25 2020 07:31:04

%S 1,2,4,10,26,72,202,580

%N Column sums of a Gaussian polynomial-shaped array. Row sums generate the Eulerian array A008292.

%C Column sums of the Gaussian polynomial template count numeric partitions. Row sums of the Gaussian polynomial template generate Pascal's triangle. A105552 has the same shape as the template and counts compositions. Row sums of the Eulerian array counts permutations of n object.

%e The column sums begin 1 2 4 10 26 72 202 580 ... because the structure of the Array begin as follows:

%e 1..................................................................

%e ......1............................................................

%e ......1............................................................

%e ............1......................................................

%e ............2......2...............................................

%e ............1......................................................

%e ..................1................................................

%e ..................3......5......3..................................

%e ..................3......5......3..................................

%e ..................1................................................

%e ............................1......................................

%e ............................4.......9.......9.......4..............

%e ............................6.......16......22......16.......6.....

%e ............................4.......9.......9.......4..............

%e ............................1......................................

%e etc.

%Y Cf. A000041, A000079, A000142, A007318, A008292, A047970, A060351, A105552.

%K nonn,more

%O 1,2

%A _Alford Arnold_, Dec 25 2006