A165257 - OEIS

A165257

Triangle in which n-th row is binomial(n+k-1,k), for column k=1..n.

1, 2, 3, 3, 6, 10, 4, 10, 20, 35, 5, 15, 35, 70, 126, 6, 21, 56, 126, 252, 462, 7, 28, 84, 210, 462, 924, 1716, 8, 36, 120, 330, 792, 1716, 3432, 6435, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24310

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OFFSET

1,2

COMMENTS

T(n,k) is the number of non-descending sequences with length k and last number is less or equal to n. T(n,k) is also the number of integer partitions (of any positive integer) with length k and largest part is less or equal to n. - Zlatko Damijanic, Dec 06 2024

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

2, 3;

3, 6, 10;

4, 10, 20, 35;

5, 15, 35, 70, 126;

6, 21, 56, 126, 252, 462;

7, 28, 84, 210, 462, 924, 1716;

MATHEMATICA

Table[Binomial[n+k-1, k], {n, 10}, {k, n}]//Flatten (* Harvey P. Dale, Jul 31 2021 *)

PROG

(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1( binomial(n+k-1, k), ", "); ); print(); ); } \\ Michel Marcus, Jun 12 2013

CROSSREFS

A059481 with the first column (k = 0) removed.

Cf. A030662 (row sums), A001700 (diagonal).

Sequence in context: A320002 A129068 A079888 * A368223 A059191 A124063

Adjacent sequences: A165254 A165255 A165256 * A165258 A165259 A165260

KEYWORD

easy,nonn,tabl

AUTHOR

Daniel McLaury (daniel.mclaury(AT)gmail.com), Sep 11 2009

STATUS

approved