A264436 Triangle read by rows, inverse Bell transform of the complementary Bell numbers (A000587); T(n,k) for n>=0 and 0<=k<=n.

1, 0, 1, 0, 1, 1, 0, 3, 3, 1, 0, 14, 15, 6, 1, 0, 89, 100, 45, 10, 1, 0, 716, 834, 405, 105, 15, 1, 0, 6967, 8351, 4284, 1225, 210, 21, 1, 0, 79524, 97596, 52220, 16009, 3080, 378, 28, 1, 0, 1041541, 1303956, 721674, 233268, 48699, 6804, 630, 36, 1

Offset: 0

Author

Peter Luschny, Dec 01 2015

Keywords

• nonn
• tabl

Examples

			Triangle starts:
1,
0,     1,
0,     1,     1,
0,     3,     3,     1,
0,    14,    15,     6,     1,
0,    89,   100,    45,    10,    1,
0,   716,   834,   405,   105,   15,   1,
0,  6967,  8351,  4284,  1225,  210,  21,  1,
0, 79524, 97596, 52220, 16009, 3080, 378, 28, 1
		

Links

• Peter Luschny, The Bell transform

Crossrefs

Cf. A000587, A007549, A029768, A264428, A264429.

Programs

Sage

# uses[bell_transform from A264428, inverse_bell_transform from A264429]
def A264436_matrix(dim):
    uno = [1]*dim
    complementary_bell_numbers = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, uno))) for n in (0..dim)]
    return inverse_bell_transform(dim, complementary_bell_numbers)
A264436_matrix(9)

Formula

Row sums are A029768(n-1) for n>=1.

T(n,1) = A007549(n) for n>=1.