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A123097 Triangle read by rows: T(n,k) = binomial(n-2, k-1) + n*binomial(n-1, k-1), 1 <= k <= n, starting with T(1, 1) = 1. 0
1, 3, 2, 4, 7, 3, 5, 14, 13, 4, 6, 23, 33, 21, 5, 7, 34, 66, 64, 31, 6, 8, 47, 115, 150, 110, 43, 7, 9, 62, 183, 300, 295, 174, 57, 8, 10, 79, 273, 539, 665, 525, 259, 73, 9, 11, 98, 388, 896, 1330, 1316, 868, 368, 91, 10, 12, 119, 531, 1404, 2436, 2898, 2394, 1356, 504, 111, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Triangle is M*P, where M is the infinite bidiagonal matrix with (1,2,3,...) in the main diagonal and (1,1,1,...) in the subdiagonal and P is Pascal's triangle as an infinite lower triangular matrix. The triangle A124727 is P*M.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

First few rows of the triangle are

  1;

  3,  2;

  4,  7,  3;

  5, 14, 13,  4

  6, 23, 33, 21,  5;

  7, 34, 66, 64, 31,  6;

  ...

MAPLE

T:=proc(n, k) if n=1 and k=1 then 1 elif n=1 then 0 else binomial(n-2, k-1)+n*binomial(n-1, k-1) fi end: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form

PROG

(PARI) T(n, k) = if ((n==1), (k==1), binomial(n-2, k-1)+n*binomial(n-1, k-1));

matrix(11, 11, n, k, T(n, k)) \\ Michel Marcus, Nov 09 2019

CROSSREFS

Row sums = A052951: (1, 5, 14, 36, 88, 208, ...).

Sequence in context: A338213 A317736 A060006 * A209706 A134571 A054086

Adjacent sequences:  A123094 A123095 A123096 * A123098 A123099 A123100

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson and Roger L. Bagula, Nov 05 2006

EXTENSIONS

Edited by N. J. A. Sloane, Nov 24 2006

STATUS

approved

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Last modified April 21 02:10 EDT 2021. Contains 343143 sequences. (Running on oeis4.)