A116672 - OEIS

A116672

Triangle read by rows in which the binomial transform of the n-th row gives the Euler transform of the n-th diagonal of Pascal's triangle (A007318).

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 6, 11, 7, 1, 1, 10, 27, 29, 12, 1, 1, 14, 57, 96, 72, 21, 1, 1, 21, 117, 277, 319, 176, 38, 1

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

OFFSET

1,5

COMMENTS

For example, the Euler transform of 1,3,6,... is 1,1,4,10,26,59,141,... (A000294) differing slightly from A000293 which counts the solid partitions.

The NAME does not reproduce the DATA, COMMENTS, or EXAMPLES. - R. J. Mathar, Jul 19 2017

The binomial transforms of the rows form the rows of A289656. - N. J. A. Sloane, Jul 19 2017

LINKS

Table of n, a(n) for n=1..36.

N. J. A. Sloane, Transforms

EXAMPLE

Row 6 is 1 10 27 29 12 1 generating 1 11 48 141 ... (A008780) the seventh term in the Euler transforms of 1,1,1,...; 1,2,3,...; 1,3,6,... 1,4,10,... etc.

Triangle begins:

1, 1;

1, 2, 1;

1, 4, 4, 1;

1, 6, 11, 7, 1;

1, 10, 27, 29, 12, 1;

1, 14, 57, 96, 72, 21, 1;

1, 21, 117, 277, 319, 176, 38, 1;

...

CROSSREFS

Cf. A000293, A116673 (row sums), A008778 - A008780, A289656.

Sequence in context: A203906 A274310 A096806 * A161126 A128562 A034368

Adjacent sequences: A116669 A116670 A116671 * A116673 A116674 A116675

KEYWORD

nonn,tabl,obsc

AUTHOR

Alford Arnold, Feb 22 2006

STATUS

approved