A108959 Triangle arising in connection with deformations of type D Kleinian singularities.
1, 2, 1, 3, 4, 2, 4, 10, 14, 7, 5, 20, 54, 76, 38, 6, 35, 154, 419, 590, 295, 7, 56, 364, 1616, 4400, 6196, 3098, 8, 84, 756, 4962, 22048, 60036, 84542, 42271, 9, 120, 1428, 12984, 85300, 379052, 1032154, 1453468, 726734, 10, 165, 2508, 30162, 274516, 1803638, 8014990, 21824737, 30733358, 15366679
Offset: 0
Examples
Triangle begins: 1; 2, 1; 3, 4, 2; 4, 10, 14, 7; 5, 20, 54, 76, 38; ...
Links
- Paul Boddington, No-cycle algebras and representation theory, Ph.D. thesis, University of Warwick, 2004.
Crossrefs
Programs
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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
Formula
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.
Extensions
More terms from Michel Marcus, Mar 18 2023