A340424 Triangle read by rows: T(n,k) = A024916(n-k+1)*A002865(k-1), 1 <= k <= n.

1, 4, 0, 8, 0, 1, 15, 0, 4, 1, 21, 0, 8, 4, 2, 33, 0, 15, 8, 8, 2, 41, 0, 21, 15, 16, 8, 4, 56, 0, 33, 21, 30, 16, 16, 4, 69, 0, 41, 33, 42, 30, 32, 16, 7, 87, 0, 56, 41, 66, 42, 60, 32, 28, 8, 99, 0, 69, 56, 82, 66, 84, 60, 56, 32, 12, 127, 0, 87, 69, 112, 82, 132, 84, 105, 64, 48, 14

Offset

1,2

Comments

Conjecture: the sum of row n equals A066186(n), the sum of all parts of all partitions of n.

Links

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

Example

Triangle begins:
   1;
   4,  0;
   8,  0,  1;
  15,  0,  4,  1;
  21,  0,  8,  4,  2;
  33,  0, 15,  8,  8,  2;
  41,  0, 21, 15, 16   8,  4;
  56,  0, 33, 21, 30, 16, 16,  4;
  69,  0, 41, 33, 42, 30, 32, 16,  7;
  87,  0, 56, 41, 66, 42, 60, 32, 28,  8;
  99,  0, 69, 56, 82, 66, 84, 60, 56, 32, 12;
...
For n = 6 the calculation of every term of row 6 is as follows:
--------------------------
k   A002865         T(6,k)
--------------------------
1      1   *  33   =  33
2      0   *  21   =   0
3      1   *  15   =  15
4      1   *   8   =   8
5      2   *   4   =   8
6      2   *   1   =   2
.           A024916
--------------------------
The sum of row 6 is 33 + 0 + 15 + 8 + 8 + 2 = 66, equaling A066186(6) = 66.

Crossrefs

Mirror of A245099.

Columns 1, 3 and 4 are A024916 (partial sums of A000203).

Column 2 gives A000004.

Columns 5 and 6 give A327329.

Columns 7 and 8 give A243980.

Leading diagonal gives A002865.

Cf. A066186.

Sequence in context: A182158 A103554 A261278 * A222609 A247848 A076261

Adjacent sequences: A340421 A340422 A340423 * A340425 A340426 A340427

Keyword

nonn,tabl

Author

Omar E. Pol, Jan 07 2021

Status

approved