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A156665 Triangle read by rows, A156663 * A007318.

%I A156665 #9 Jun 02 2025 01:22:18
%S A156665 1,1,1,3,2,1,3,5,3,1,7,8,8,4,1,7,15,16,12,5,1,15,22,31,28,17,6,1,15,
%T A156665 37,53,59,45,23,7,1,31,52,90,112,104,68,30,8,1,31,83,142,202,216,172,
%U A156665 98,38,9,1,63,114,225,344,418,388,270,136,47,10,1
%N A156665 Triangle read by rows, A156663 * A007318.
%C A156665 Row sums = A122746: (1, 2, 6, 12, 28, 56, 120,...).
%H A156665 Robert Israel, <a href="/A156665/b156665.txt">Table of n, a(n) for n = 0..10010</a> (first 141 rows, flattened)
%F A156665 Triangle read by rows, A156663 * A007318
%F A156665 G.f. for triangle: 1/((1-2*x^2)*(1-x-x*y)). - _Robert Israel_, Aug 10 2015
%e A156665 First few rows of the triangle =
%e A156665 1;
%e A156665 1, 1;
%e A156665 3, 2, 1;
%e A156665 3, 5, 3, 1;
%e A156665 7, 8, 8, 4, 1;
%e A156665 7, 15, 16, 12, 5, 1;
%e A156665 15, 22, 31, 28, 17, 6, 1;
%e A156665 15, 37, 53, 59, 45, 23, 7, 1;
%e A156665 31, 52, 90, 112, 104, 68, 30, 8, 1;
%e A156665 31, 83, 142, 202, 216, 172, 98, 38, 9, 1;
%e A156665 63, 114, 225, 344, 418, 388, 270, 136, 47, 10, 1;
%e A156665 ...
%p A156665 N:= 12: # for the first N rows
%p A156665 A156663:= Matrix(N,N,(i,j) -> `if`((i-j)::even, 2^((i-j)/2),0), shape=triangular[lower]):
%p A156665 A007318:= Matrix(N,N,(i,j) -> binomial(i-1,j-1),shape=triangular[lower]):
%p A156665 P:= A156663 . A007318:
%p A156665 seq(seq(P[i,j],j=1..i),i=1..N); # _Robert Israel_, Aug 10 2015
%Y A156665 A156663, A122746
%K A156665 nonn,tabl
%O A156665 0,4
%A A156665 _Gary W. Adamson_, Feb 12 2009