cp's OEIS Frontend

A210489 Array read by ascending antidiagonals where row n contains the second partial sums of row n of Pascal's triangle.

%I A210489 #26 Apr 29 2020 10:02:51
%S A210489 1,1,2,1,3,3,1,4,5,4,1,5,8,7,5,1,6,12,12,9,6,1,7,17,20,16,11,7,1,8,23,
%T A210489 32,28,20,13,8,1,9,30,49,48,36,24,15,9,1,10,38,72,80,64,44,28,17,10,1,
%U A210489 11,47,102,129,112,80,52,32,19,11,1,12,57,140,201,192,144,96,60,36,21,12
%N A210489 Array read by ascending antidiagonals where row n contains the second partial sums of row n of Pascal's triangle.
%C A210489 Appears to be a transposed version of A188553 with a leading column of 1's.
%H A210489 Andrew Howroyd, <a href="/A210489/b210489.txt">Table of n, a(n) for n = 0..1325</a>
%F A210489 T(n,k) = A193605(n,k).
%F A210489 T(n,m) = Sum_{k=1..m} k*binomial(n,m-k). - _Vladimir Kruchinin_, Apr 06 2018
%e A210489 Table starts:
%e A210489 1,  2,   3,     4,      5,      6,      7,      8,      9,     10
%e A210489 1,  3,   5,     7,      9,     11,     13,     15,     17,     19
%e A210489 1,  4,   8,    12,     16,     20,     24,     28,     32,     36
%e A210489 1,  5,  12,    20,     28,     36,     44,     52,     60,     68
%e A210489 1,  6,  17,    32,     48,     64,     80,     96,    112,    128
%e A210489 1,  7,  23,    49,     80,    112,    144,    176,    208,    240
%e A210489 1,  8,  30,    72,    129,    192,    256,    320,    384,    448
%e A210489 1,  9,  38,   102,    201,    321,    448,    576,    704,    832
%e A210489 1, 10,  47,   140,    303,    522,    769,   1024,   1280,   1536
%e A210489 1, 11,  57,   187,    443,    825,   1291,   1793,   2304,   2816
%e A210489 1, 12,  68,   244,    630,   1268,   2116,   3084,   4097,   5120
%e A210489 1, 13,  80,   312,    874,   1898,   3384,   5200,   7181,   9217
%e A210489 1, 14,  93,   392,   1186,   2772,   5282,   8584,  12381,  16398
%e A210489 1, 15, 107,   485,   1578,   3958,   8054,  13866,  20965,  28779
%e A210489 1, 16, 122,   592,   2063,   5536,  12012,  21920,  34831,  49744
%e A210489 1, 17, 138,   714,   2655,   7599,  17548,  33932,  56751,  84575
%e A210489 1, 18, 155,   852,   3369,  10254,  25147,  51480,  90683, 141326
%e A210489 1, 19, 173,  1007,   4221,  13623,  35401,  76627, 142163, 232009
%e A210489 1, 20, 192,  1180,   5228,  17844,  49024, 112028, 218790, 374172
%e A210489 1, 21, 212,  1372,   6408,  23072,  66868, 161052, 330818, 592962
%e A210489 1, 22, 233,  1584,   7780,  29480,  89940, 227920, 491870, 923780
%e A210489 1, 23, 255,  1817,   9364,  37260, 119420, 317860, 719790,1415650
%e A210489 1, 24, 278,  2072,  11181,  46624, 156680, 437280,1037650,2135440
%e A210489 1, 25, 302,  2350,  13253,  57805, 203304, 593960,1474930,3173090
%e A210489 1, 26, 327,  2652,  15603,  71058, 261109, 797264,2068890,4648020
%e A210489 1, 27, 353,  2979,  18255,  86661, 332167,1058373,2866154,6716910
%e A210489 1, 28, 380,  3332,  21234, 104916, 418828,1390540,3924527,9583064
%o A210489 (PARI) T(n,m) = {sum(k=1, m, k*binomial(n,m-k))}
%o A210489 { for(n=0, 10, for(m=1, 10, print1(T(n,m), ", ")); print) } \\ _Andrew Howroyd_, Apr 28 2020
%Y A210489 Cf. A104734, A132379 (another transposed variant), A188553, A193605.
%K A210489 nonn,tabl,easy
%O A210489 0,3
%A A210489 _Jakub Jaroslaw Ciaston_, Jan 23 2013
%E A210489 Offset corrected and terms a(55) and beyond from _Andrew Howroyd_, Apr 28 2020