cp's OEIS Frontend

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

%I A011972 #30 Dec 02 2023 05:09:49
%S A011972 1,2,3,5,7,10,15,20,27,37,52,67,87,114,151,203,255,322,409,523,674,
%T A011972 877,1080,1335,1657,2066,2589,3263,4140,5017,6097,7432,9089,11155,
%U A011972 13744,17007,21147,25287,30304,36401,43833,52922,64077,77821,94828
%N A011972 Sequence formed by reading rows of triangle defined in A011971.
%C A011972 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]
%H A011972 Chai Wah Wu, <a href="/A011972/b011972.txt">Rows n = 0..200, flattened</a>
%e A011972 Triangle T(n, k) begins:
%e A011972 [0]   1;
%e A011972 [1]   2,    3;
%e A011972 [2]   5,    7,   10;
%e A011972 [3]  15,   20,   27,   37;
%e A011972 [4]  52,   67,   87,  114,  151;
%e A011972 [5] 203,  255,  322,  409,  523,  674;
%e A011972 [6] 877, 1080, 1335, 1657, 2066, 2589, 3263;
%e A011972 ...
%p A011972 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
%t A011972 T[n_, k_] := Sum[Binomial[k, i] BellB[n - k + i + 1], {i, 0, k}];
%t A011972 Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Nov 19 2019 *)
%o A011972 (Python)
%o A011972 from itertools import accumulate
%o A011972 A011972_list = blist = [1]
%o A011972 for _ in range(10**2):
%o A011972     b = blist[-1]
%o A011972     blist = list(accumulate([b]+blist))
%o A011972     A011972_list += blist[1:]
%o A011972 # _Chai Wah Wu_, Sep 02 2014, updated _Chai Wah Wu_, Sep 20 2014
%K A011972 nonn,easy,tabl
%O A011972 0,2
%A A011972 _N. J. A. Sloane_ and _J. H. Conway_