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%I #20 Jul 19 2017 10:28:09
%S 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,
%T 21,117,277,319,176,38,1
%N 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).
%C 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.
%C The NAME does not reproduce the DATA, COMMENTS, or EXAMPLES. - _R. J. Mathar_, Jul 19 2017
%C The binomial transforms of the rows form the rows of A289656. - _N. J. A. Sloane_, Jul 19 2017
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%e 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.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 4, 4, 1;
%e 1, 6, 11, 7, 1;
%e 1, 10, 27, 29, 12, 1;
%e 1, 14, 57, 96, 72, 21, 1;
%e 1, 21, 117, 277, 319, 176, 38, 1;
%e ...
%Y Cf. A000293, A116673 (row sums), A008778 - A008780, A289656.
%K nonn,tabl,obsc
%O 1,5
%A _Alford Arnold_, Feb 22 2006