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A212362 Triangle by rows, binomial transform of the beheaded Pascal's triangle A074909; and relating to the Bernoulli numbers. 1
1, 2, 2, 4, 7, 3, 8, 19, 15, 4, 16, 47, 52, 26, 5, 32, 111, 155, 110, 40, 6, 64, 155, 426, 385, 200, 57, 7, 128, 575, 1113, 1211, 805, 329, 77, 8, 256, 1279, 2808, 3556, 2856, 1498, 504, 100, 9, 512, 2815, 6903, 9948, 9324, 5922, 2562, 732, 126, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of the triangle inverse = A027641/A027642, the Bernoulli numbers; (1, -1/2, 1/6, 0, -1/30,...)

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Binomial transform of the beheaded Pascal's triangle (A074909) as a matrix. (The beheaded Pascal matrix deletes the rightmost border of 1's.)

EXAMPLE

First few rows of the triangle are:

1;

2, 2;

4, 7, 3;

8, 19, 15, 4

16, 47, 52, 26, 5;

32, 111, 155, 110, 40, 6;

64, 255, 426, 385, 200, 57, 7;

128, 575, 1113, 1211, 805, 329, 77, 8;

256, 1279, 2808, 3556, 2856, 1498, 504, 100, 9;

...

MAPLE

A212362 := proc(n, k)

        add( binomial(n, i)*A074909(i, k), i=0..n) ;

end proc: # R. J. Mathar, Aug 03 2015

CROSSREFS

Cf. A074909, A027641/A027642, A027649 (row sums), A006589 (2nd column).

Sequence in context: A249758 A157470 A120280 * A209142 A115754 A210600

Adjacent sequences:  A212359 A212360 A212361 * A212363 A212364 A212365

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 29 2012

STATUS

approved

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Last modified March 22 23:04 EDT 2019. Contains 321422 sequences. (Running on oeis4.)