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A332601 An RNA-type Riordan lower-triangular matrix, read by rows.

%I A332601 #16 Feb 25 2025 13:12:14
%S A332601 1,1,1,2,2,1,4,4,3,1,8,9,7,4,1,17,20,17,11,5,1,37,45,41,29,16,6,1,82,
%T A332601 103,98,75,46,22,7,1,185,238,235,190,127,69,29,8,1,423,555,565,477,
%U A332601 340,203,99,37,9,1,978,1305,1362,1192,893,573,310,137,46,10,1
%N A332601 An RNA-type Riordan lower-triangular matrix, read by rows.
%H A332601 Andrew Howroyd, <a href="/A332601/b332601.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%H A332601 Tian-Xiao He, <a href="https://doi.org/10.1016/j.disc.2019.111718">A-sequences, Z-sequence, and B-sequences of Riordan matrices</a>, Discrete Mathematics 343.3 (2020): 111718. Also <a href="https://arxiv.org/abs/1909.02639">arXiv preprint</a>, arXiv:1909.02639 [math.CO], 2019.
%e A332601 Triangle begins:
%e A332601    1;
%e A332601    1,  1;
%e A332601    2,  2,  1;
%e A332601    4,  4,  3,  1;
%e A332601    8,  9,  7,  4,  1;
%e A332601   17, 20, 17, 11,  5, 1;
%e A332601   37, 45, 41, 29, 16, 6, 1;
%e A332601   ...
%o A332601 (PARI) \\ ColGf gives the g.f. of the k-th column.
%o A332601 ColGf(k,n)={my(g=(1 - x + x^2 - sqrt(1 - 2*x - x^2 - 2*x^3 + x^4 + O(x^(n-k+4))))/(2*x^2)); (g - 1)/x*(x*g)^k}
%o A332601 T(n,k) = {polcoef(ColGf(k,n), n)} \\ _Andrew Howroyd_, Mar 02 2023
%Y A332601 Cf. A110438.
%K A332601 nonn,tabl
%O A332601 0,4
%A A332601 _N. J. A. Sloane_, Mar 06 2020
%E A332601 Terms a(28) and beyond from _Andrew Howroyd_, Mar 02 2023