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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.

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 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`Appears to be a transposed version of A188553 with a leading column of 1's.`
	LINKS	`Andrew Howroyd, Table of n, a(n) for n = 0..1325`
	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: A208777 A104732 A132108 * A344821 A125175 A210552` `Adjacent sequences: A210486 A210487 A210488 * A210490 A210491 A210492`
	KEYWORD	`nonn,tabl,easy`
	AUTHOR	`Jakub Jaroslaw Ciaston, Jan 23 2013`
	EXTENSIONS	`Offset corrected and terms a(55) and beyond from Andrew Howroyd, Apr 28 2020`
	STATUS	`approved`

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Last modified August 29 15:03 EDT 2024. Contains 375517 sequences. (Running on oeis4.)