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A210489
Array read by ascending antidiagonals where row n contains the second partial sums of row n of Pascal's triangle.
2
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, 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, 11, 47, 102, 129, 112, 80, 52, 32, 19, 11, 1, 12, 57, 140, 201, 192, 144, 96, 60, 36, 21, 12
OFFSET
0,3
COMMENTS
Appears to be a transposed version of A188553 with a leading column of 1's.
LINKS
FORMULA
T(n,k) = A193605(n,k).
T(n,m) = Sum_{k=1..m} k*binomial(n,m-k). - Vladimir Kruchinin, Apr 06 2018
EXAMPLE
Table starts:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1, 3, 5, 7, 9, 11, 13, 15, 17, 19
1, 4, 8, 12, 16, 20, 24, 28, 32, 36
1, 5, 12, 20, 28, 36, 44, 52, 60, 68
1, 6, 17, 32, 48, 64, 80, 96, 112, 128
1, 7, 23, 49, 80, 112, 144, 176, 208, 240
1, 8, 30, 72, 129, 192, 256, 320, 384, 448
1, 9, 38, 102, 201, 321, 448, 576, 704, 832
1, 10, 47, 140, 303, 522, 769, 1024, 1280, 1536
1, 11, 57, 187, 443, 825, 1291, 1793, 2304, 2816
1, 12, 68, 244, 630, 1268, 2116, 3084, 4097, 5120
1, 13, 80, 312, 874, 1898, 3384, 5200, 7181, 9217
1, 14, 93, 392, 1186, 2772, 5282, 8584, 12381, 16398
1, 15, 107, 485, 1578, 3958, 8054, 13866, 20965, 28779
1, 16, 122, 592, 2063, 5536, 12012, 21920, 34831, 49744
1, 17, 138, 714, 2655, 7599, 17548, 33932, 56751, 84575
1, 18, 155, 852, 3369, 10254, 25147, 51480, 90683, 141326
1, 19, 173, 1007, 4221, 13623, 35401, 76627, 142163, 232009
1, 20, 192, 1180, 5228, 17844, 49024, 112028, 218790, 374172
1, 21, 212, 1372, 6408, 23072, 66868, 161052, 330818, 592962
1, 22, 233, 1584, 7780, 29480, 89940, 227920, 491870, 923780
1, 23, 255, 1817, 9364, 37260, 119420, 317860, 719790,1415650
1, 24, 278, 2072, 11181, 46624, 156680, 437280,1037650,2135440
1, 25, 302, 2350, 13253, 57805, 203304, 593960,1474930,3173090
1, 26, 327, 2652, 15603, 71058, 261109, 797264,2068890,4648020
1, 27, 353, 2979, 18255, 86661, 332167,1058373,2866154,6716910
1, 28, 380, 3332, 21234, 104916, 418828,1390540,3924527,9583064
PROG
(PARI) T(n, m) = {sum(k=1, m, k*binomial(n, m-k))}
{ for(n=0, 10, for(m=1, 10, print1(T(n, m), ", ")); print) } \\ Andrew Howroyd, Apr 28 2020
CROSSREFS
Cf. A104734, A132379 (another transposed variant), A188553, A193605.
Sequence in context: A104732 A132108 A377000 * A344821 A125175 A210552
KEYWORD
nonn,tabl,easy
AUTHOR
EXTENSIONS
Offset corrected and terms a(55) and beyond from Andrew Howroyd, Apr 28 2020
STATUS
approved