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A091595 Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k) * 2^k.

%I A091595 #15 Sep 06 2023 06:57:49
%S A091595 1,1,1,3,2,1,5,5,3,1,11,12,8,4,1,21,27,22,12,5,1,43,62,55,36,17,6,1,
%T A091595 85,137,137,99,55,23,7,1,171,304,330,264,164,80,30,8,1,341,663,784,
%U A091595 682,466,256,112,38,9,1,683,1442,1833,1720,1278,772,382,152,47,10,1,1365,3109,4235,4257,3402,2234,1218,550,201,57,11,1
%N A091595 Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k) * 2^k.
%C A091595 A Jacobsthal related number number triangle.
%H A091595 Seiichi Manyama, <a href="/A091595/b091595.txt">Rows n = 0..139, flattened</a>
%F A091595 k-th column has g.f. 1/(1-x-2x^2) * ( x*(1-2x^2)/(1-x-2x^2) )^k.
%e A091595 Rows begin:
%e A091595    1,
%e A091595    1,   1,
%e A091595    3,   2,   1,
%e A091595    5,   5,   3,  1,
%e A091595   11,  12,   8,  4,  1,
%e A091595   21,  27,  22, 12,  5,  1,
%e A091595   43,  62,  55, 36, 17,  6, 1,
%e A091595   85, 137, 137, 99, 55, 23, 7, 1,
%e A091595   ...
%Y A091595 Columns include A001045, A091596. Row sums are A077937.
%K A091595 easy,nonn,tabl
%O A091595 0,4
%A A091595 _Paul Barry_, Jan 23 2004