This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177976 #33 Jun 12 2021 09:06:50
%S A177976 1,1,1,1,2,1,1,4,3,1,1,6,8,4,1,1,10,15,13,5,1,1,12,29,29,19,6,1,1,18,
%T A177976 42,63,49,26,7,1,1,22,69,106,118,76,34,8,1,1,28,95,189,225,201,111,43,
%U A177976 9,1,1,32,134,289,434,427,320,155,53,10,1,1,42,172,444,729,888,748,484,209,64,11,1
%N A177976 Square array T(n,k) read by antidiagonals up. Cumulative column sums of A177975.
%C A177976 Each row is described by both a binomial expression and a closed form polynomial. The closed form polynomials given in A177977 extends this table to the left. For example the 0th column is A002321 and the -1st column is A092149.
%C A177976 Also number of ordered k-tuples of integers from [ 1..n ] with no global factor. - _Seiichi Manyama_, Jun 12 2021
%H A177976 Seiichi Manyama, <a href="/A177976/b177976.txt">Antidiagonals n = 1..140, flattened</a>
%F A177976 From _Seiichi Manyama_, Jun 12 2021: (Start)
%F A177976 G.f. of column k: (1/(1 - x)) * Sum_{j>=1} mu(j) * x^j/(1 - x^j)^k.
%F A177976 T(n,k) = Sum_{j=1..n} Sum_{d|j} mu(j/d) * binomial(d+k-2,d-1).
%F A177976 T(n,k) = binomial(n+k-1,k) - Sum_{j=2..n} T(floor(n/j),k). (End)
%e A177976 Table begins:
%e A177976 1..1...1....1.....1.....1......1......1.......1.......1.......1
%e A177976 1..2...3....4.....5.....6......7......8.......9......10......11
%e A177976 1..4...8...13....19....26.....34.....43......53......64......76
%e A177976 1..6..15...29....49....76....111....155.....209.....274.....351
%e A177976 1.10..29...63...118...201....320....484.....703.....988....1351
%e A177976 1.12..42..106...225...427....748...1233....1937....2926....4278
%e A177976 1.18..69..189...434...888...1671...2948....4939....7930...12285
%e A177976 1.22..95..289...729..1624...3303...6260...11209...19150...31447
%e A177976 1.28.134..444..1209..2890...6278..12659...24034...43405...75139
%e A177976 1.32.172..626..1850..4761..11067..23762...47841...91301..166506
%e A177976 1.42.237..911..2850..7763..19074..43209...91598..183678..351261
%e A177976 1.46.287.1203..4059.11829..30911..74129..165737..349426..700699
%e A177976 1.58.377.1657..5878.18016..49474.124516..291706..643355.1347344
%e A177976 1.64.452.2130..8044.26117..75676.200313..492185.1135761.2483392
%e A177976 1.72.552.2766.11020.37599.114199.316228..811416.1952182.4443582
%e A177976 1.80.652.3462.14566.52311.166747.483340.1295295.3248246.7692894
%o A177976 (PARI) T(n, k) = sum(j=1, n, sumdiv(j, d, moebius(j/d)*binomial(d+k-2, d-1))); \\ _Seiichi Manyama_, Jun 12 2021
%o A177976 (PARI) T(n, k) = binomial(n+k-1, k)-sum(j=2, n, T(n\j, k)); \\ _Seiichi Manyama_, Jun 12 2021
%Y A177976 Column k=1..5 gives A000012, A002088, A015631, A015634, A015650.
%Y A177976 Cf. A177975, A177977, A344527, A345229.
%K A177976 nonn,tabl
%O A177976 1,5
%A A177976 _Mats Granvik_, May 16 2010