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A011972
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Sequence formed by reading rows of triangle defined in A011971.
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5
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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]
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LINKS
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EXAMPLE
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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;
...
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MAPLE
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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
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MATHEMATICA
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T[n_, k_] := Sum[Binomial[k, i] BellB[n - k + i + 1], {i, 0, k}];
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PROG
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(Python)
from itertools import accumulate
for _ in range(10**2):
b = blist[-1]
blist = list(accumulate([b]+blist))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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