A371994 Triangle read by rows: Related to the Euler numbers.

1, 0, 1, 0, 1, 5, 0, 1, 19, 61, 0, 1, 42, 498, 1385, 0, 1, 74, 1932, 19238, 50521, 0, 1, 115, 5290, 114830, 1057475, 2702765, 0, 1, 165, 11805, 449539, 8949633, 79160457, 199360981, 0, 1, 224, 23016, 1360198, 47306246, 899141244, 7768928932, 19391512145

Offset: 0

Author

Peter Luschny, Apr 21 2024

Keywords

• nonn
• tabl

Comments

Inspired by Philippe Deléham's formula for A371637.

Examples

			Triangle starts:
  [0] [1]
  [1] [0, 1]
  [2] [0, 1,   5]
  [3] [0, 1,  19,    61]
  [4] [0, 1,  42,   498,   1385]
  [5] [0, 1,  74,  1932,  19238,   50521]
  [6] [0, 1, 115,  5290, 114830, 1057475,  2702765]
  [7] [0, 1, 165, 11805, 449539, 8949633, 79160457, 199360981]
		

Crossrefs

Cf. A000364 (main diagonal), A371637, A371765 (row sums), A372001.

Cf. A084938.

Programs

SageMath

# Using function GeneralizedDelehamDelta from A372001.
def A371994_triangle(dim):
    a = lambda n: n % 2
    b = lambda n: (n + 1)^2
    return GeneralizedDelehamDelta([a, b], dim, False)
for row in A371994_triangle(8): print(row)

Formula

Triangle T given by [0, 1, 0, 1, 0, 1, 0, 1, ...] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined by Deléham in A084938.