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A091594 Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k).

%I A091594 #16 Sep 06 2023 06:57:53
%S A091594 1,1,1,2,2,1,3,4,3,1,5,8,7,4,1,8,15,16,11,5,1,13,28,34,28,16,6,1,21,
%T A091594 51,70,66,45,22,7,1,34,92,140,148,116,68,29,8,1,55,164,274,320,281,
%U A091594 190,98,37,9,1,89,290,527,672,651,494,295,136,46,10,1,144,509,999,1379,1456,1219,819,439,183,56,11,1
%N A091594 Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k).
%C A091594 A Fibonacci related number triangle.
%H A091594 Seiichi Manyama, <a href="/A091594/b091594.txt">Rows n = 0..139, flattened</a>
%F A091594 k-th column has g.f. 1/(1-x-x^2) * ( x*(1-x^2)/(1-x-x^2) )^k.
%e A091594 Rows begin:
%e A091594    1,
%e A091594    1,  1,
%e A091594    2,  2,  1,
%e A091594    3,  4,  3,  1,
%e A091594    5,  8,  7,  4,  1,
%e A091594    8, 15, 16, 11,  5,  1,
%e A091594   13, 28, 34, 28, 16,  6, 1,
%e A091594   21, 51, 70, 66, 45, 22, 7, 1,
%e A091594   ...
%Y A091594 Columns include A000045, A029907, A054455. Row sums are A006054.
%K A091594 easy,nonn,tabl
%O A091594 0,4
%A A091594 _Paul Barry_, Jan 23 2004