A011972 Sequence formed by reading rows of triangle defined in A011971.

1, 2, 3, 5, 7, 10, 15, 20, 27, 37, 52, 67, 87, 114, 151, 203, 255, 322, 409, 523, 674, 877, 1080, 1335, 1657, 2066, 2589, 3263, 4140, 5017, 6097, 7432, 9089, 11155, 13744, 17007, 21147, 25287, 30304, 36401, 43833, 52922, 64077, 77821, 94828

Offset: 0

Author

N. J. A. Sloane and J. H. Conway

Keywords

• nonn
• easy
• tabl

Comments

Terms that are repeated in A011971 are included only once. In other words, dropping the elements on the diagonal and reading by rows gives this sequence. [Joerg Arndt, May 31 2013]

Examples

			Triangle T(n, k) begins:
[0]   1;
[1]   2,    3;
[2]   5,    7,   10;
[3]  15,   20,   27,   37;
[4]  52,   67,   87,  114,  151;
[5] 203,  255,  322,  409,  523,  674;
[6] 877, 1080, 1335, 1657, 2066, 2589, 3263;
...
		

Links

• Chai Wah Wu, Rows n = 0..200, flattened

Programs

Maple

T := (n, k) -> local i; add(binomial(k, i)*combinat:-bell(n - k + i + 1), i = 0..k): seq(seq(T(n, k), k=0..n), n = 0..9);  # Peter Luschny, Dec 02 2023

Mathematica

T[n_, k_] := Sum[Binomial[k, i] BellB[n - k + i + 1], {i, 0, k}];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 19 2019 *)

Python

from itertools import accumulate
A011972_list = blist = [1]
for _ in range(10**2):
    b = blist[-1]
    blist = list(accumulate([b]+blist))
    A011972_list += blist[1:]
# Chai Wah Wu, Sep 02 2014, updated Chai Wah Wu, Sep 20 2014