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