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A108959 Triangle arising in connection with deformations of type D Kleinian singularities.

%I A108959 #19 Mar 18 2023 05:36:47
%S A108959 1,2,1,3,4,2,4,10,14,7,5,20,54,76,38,6,35,154,419,590,295,7,56,364,
%T A108959 1616,4400,6196,3098,8,84,756,4962,22048,60036,84542,42271,9,120,1428,
%U A108959 12984,85300,379052,1032154,1453468,726734,10,165,2508,30162,274516,1803638,8014990,21824737,30733358,15366679
%N A108959 Triangle arising in connection with deformations of type D Kleinian singularities.
%H A108959 Paul Boddington, <a href="http://wrap.warwick.ac.uk/3482/">No-cycle algebras and representation theory</a>, Ph.D. thesis, University of Warwick, 2004.
%F A108959 For k>=0 define p_k(x) = x(x+1)(x+3)...(x+k(k-1)/2) and consider the linear map taking each p_k(x) to k*p_k(x)/x. Then the images of x, x^2, x^3, ... are given by the rows. E.g., x^3 goes to 3x^2 + 4x + 2.
%e A108959 Triangle begins:
%e A108959   1;
%e A108959   2,  1;
%e A108959   3,  4,  2;
%e A108959   4, 10, 14,  7;
%e A108959   5, 20, 54, 76, 38;
%e A108959   ...
%o A108959 (PARI) tabl(nn) = my(v = vector(nn)); for (n=1, nn, my(p=prod(i=1, n, x+i*(i-1)/2), q=n*p/x); v[n] = q - sum(i=1, n-1, polcoeff(p, i)*v[i])); vector(nn, k, Vec(v[k])); \\ _Michel Marcus_, Mar 18 2023
%Y A108959 This sequence is an improved version of A097418. Coefficients of 1 give A000366.
%Y A108959 Cf. A128813 (the p_k polynomials).
%K A108959 easy,nonn,tabl
%O A108959 0,2
%A A108959 _Paul Boddington_, Jul 22 2005
%E A108959 More terms from _Michel Marcus_, Mar 18 2023