

A132108


Triangle T(n,k) = binomial(n,k)+nk read by rows.


2



1, 2, 1, 3, 3, 1, 4, 5, 4, 1, 5, 7, 8, 5, 1, 6, 9, 13, 12, 6, 1, 7, 11, 19, 23, 17, 7, 1, 8, 13, 26, 39, 38, 23, 8, 1, 9, 15, 34, 61, 74, 59, 30, 9, 1, 10, 17, 43, 90, 131, 130, 87, 38, 10, 1
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OFFSET

0,2


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..5000


FORMULA

T(n,k) = A007318(n,k) + A002024(n,k)  A002260(n,k).


EXAMPLE

First few rows of the triangle are:
1;
2, 1;
3, 3, 1;
4, 5, 4, 1;
5, 7, 8, 5, 1;
6, 9, 13, 12, 6, 1;
7, 11, 19, 23, 17, 7, 1;
...


MATHEMATICA

Table[Binomial[n, k]+nk, {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 08 2018 *)


PROG

(MAGMA) /* As triangle: */ [[Binomial(n, k)+nk: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, May 23 2016


CROSSREFS

Cf. A007318, A002024, A002260, A132109 (row sums).
Sequence in context: A208721 A208777 A104732 * A210489 A125175 A210552
Adjacent sequences: A132105 A132106 A132107 * A132109 A132110 A132111


KEYWORD

nonn,easy,tabl


AUTHOR

Gary W. Adamson, Aug 09 2007


STATUS

approved



