Paul Zinn-Justin has authored 4 sequences.
A247591
Dimension of invariants of 2n-th tensor power of 6-dimensional irreducible representation of A_3.
Original entry on oeis.org
1, 1, 3, 16, 126, 1296, 16071, 228514, 3607890, 61891050, 1135871490, 22049362440, 448790912004, 9512960347260, 208858963314735, 4728736078065810, 110006925920592810, 2621619942885055530, 63840054782606886630, 1585094577104979776880, 40054740803371374834780, 1028483346608802276173280
Offset: 0
For 2n=6, there are 15 invariants corresponding to all ways of pairing the 6 indices with the metric tensor, plus one invariant which is the completely skew-symmetric 6-index tensor.
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a[0] = 1; a[1] = 1; a[n_] := a[n] = (4*n*(2*n-1)*(5*n+7)*a[n-1] - 36*(n-1)*(2*n-3)*(2*n-1)*a[n-2]) / ((n+2)*(n+3)^2); Table[a[n], {n, 0, 21}]
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N=66; v=vector(N); v[1]=1; v[2]=1;
for(n=2, N-1, my(t=n+1); v[t] = (-36*(n-1)*(2*n-3)*(2*n-1)*v[t-2] + 4*n*(2*n-1)*(5*n+7)*v[t-1]) / ((n+2)*(n+3)^2) );
v \\ Joerg Arndt, Sep 20 2014
A130306
Degree of the scheme of n X n complex matrices that square to zero.
Original entry on oeis.org
1, 2, 2, 12, 28, 440, 2456, 98448, 1327632, 134302752, 4398726432, 1116577758912, 89104889764288, 56558827752672128, 11021135122877392256, 17451895365397015875840, 8316834448188073547563264, 32799202036840274283669160448, 38271513084756431661704424923648
Offset: 0
In size 1, the scheme {x^2=0} is of degree 2. in size 2, the scheme of matrices {{m11,m12},{m21,m22}} that square to zero is generically reduced and the corresponding reduced scheme is given by the equations m11+m22=0 and m11^2+m12 m21=0, hence also of degree 2.
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a[1] = 2; a[n_] := If[EvenQ[n], 2^(n/2) Det[Table[Binomial[2i + 2j + 1, 2i], {i, 0, n/2-1}, {j, 0, n/2-1}]], 2^((n-1)/2+1) Det[Table[Binomial[2i + 2j + 3, 2i + 1], {i, 0, (n-1)/2-1}, {j, 0, (n-1)/2-1}]]];
Array[a, 12] (* Jean-François Alcover, Dec 04 2018 *)
A130294
Degree of the n X n Brauer loop scheme. Also, the sum of components of the Brauer loop model in size n.
Original entry on oeis.org
1, 1, 1, 3, 7, 55, 307, 6153, 82977, 4196961, 137460201, 17446527483, 1392263902567, 441865841817751, 86102618147479627, 68171466271082093265, 32487634563234662295169, 64060941478203660710291329, 74749048993664905589266454929, 366627599282115135074804792982963
Offset: 0
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a[n_] := Which[n == 0, 1, n == 1, 1, EvenQ[n], Det[Table[Binomial[2i + 2j + 1, 2i], {i, 0, n/2 - 1}, {j, 0, n/2 - 1}]], True, Det[Table[Binomial[2i + 2j + 3, 2i + 1], {i, 0, (n-1)/2 - 1}, {j, 0, (n-1)/2 - 1}]]];
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Dec 14 2018 *)
A107445
Number of 4n X 4n alternating-sign matrices of type UU.
Original entry on oeis.org
1, 5, 198, 63206, 163170556, 3410501048325, 577465332522075000, 792313244775191409073200, 8810729389390415079342840510816
Offset: 0
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