A124931 - OEIS

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A124931

Triangle read by rows: T(n,k) = (2*k-1)*binomial(n,k) (1 <= k <= n).

1, 2, 3, 3, 9, 5, 4, 18, 20, 7, 5, 30, 50, 35, 9, 6, 45, 100, 105, 54, 11, 7, 63, 175, 245, 189, 77, 13, 8, 84, 280, 490, 504, 308, 104, 15, 9, 108, 420, 882, 1134, 924, 468, 135, 17, 10, 135, 600, 1470, 2268, 2310, 1560, 675, 170, 19, 11, 165, 825, 2310, 4158, 5082, 4290, 2475, 935, 209, 21

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

OFFSET

1,2

COMMENTS

Sum of entries in row n = 1 + (n-1)*2^n = A000337(n).

LINKS

G. C. Greubel, Rows n = 1..100 of triangle, flattened

EXAMPLE

First few rows of the triangle:

2, 3;

3, 9, 5;

4, 18, 20, 7;

5, 30, 50, 35, 9;

6, 45, 100, 105, 54, 11;

...

MAPLE

T:=(n, k)->(2*k-1)*binomial(n, k): for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form

MATHEMATICA

Table[(2*k-1)*Binomial[n, k], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Nov 19 2019 *)

PROG

(PARI) for(n=1, 12, for(k=1, n, print1((2*k-1)*binomial(n, k), ", "))) \\ G. C. Greubel, Jun 08 2017

(Magma) [(2*k-1)*Binomial(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 19 2019

(Sage) [[(2*k-1)*binomial(n, k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Nov 19 2019

(GAP) Flat(List([1..12], n-> List([1..n], k-> (2*k-1)*Binomial(n, k) ))); # G. C. Greubel, Nov 19 2019

CROSSREFS

Cf. A000337.

Sequence in context: A059083 A207626 A232324 * A210226 A209163 A124932

Adjacent sequences: A124928 A124929 A124930 * A124932 A124933 A124934

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 12 2006

EXTENSIONS

Edited by N. J. A. Sloane, Nov 29 2006

STATUS

approved