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A210489 Array read by antidiagonals where row n contains the second partial sums of row n of Pascal's triangle. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Appears to be a transposed version of A188553 with a leading column of 1's.

LINKS

Table of n, a(n) for n=1..55.

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

CROSSREFS

Cf. A104734, A132379 (another transposed variant), A188553, A193605.

Sequence in context: A208777 A104732 A132108 * A125175 A210552 A193376

Adjacent sequences:  A210486 A210487 A210488 * A210490 A210491 A210492

KEYWORD

nonn,tabl,easy

AUTHOR

Jakub Jaroslaw Ciaston, Jan 23 2013

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)