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 A356482 a(n) is the hafnian of a symmetric Toeplitz matrix M(2*n) whose first row consists of 2*n, 2*n-1, ..., 1. 7
 1, 1, 16, 714, 62528, 9056720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Wikipedia, Hafnian Wikipedia, Symmetric matrix Wikipedia, Toeplitz Matrix EXAMPLE a(2) = 16 because the hafnian of 4 3 2 1 3 4 3 2 2 3 4 3 1 2 3 4 equals M_{1,2}*M_{3,4} + M_{1,3}*M_{2,4} + M_{1,4}*M_{2,3} = 16. MATHEMATICA k[i_]:=i; M[i_, j_, n_]:=Part[Part[ToeplitzMatrix[Reverse[Array[k, n]]], i], j]; a[n_]:=Sum[Product[M[Part[PermutationList[s, 2n], 2i-1], Part[PermutationList[s, 2n], 2i], 2n], {i, n}], {s, SymmetricGroup[2n]//GroupElements}]/(n!*2^n); Array[a, 6, 0] CROSSREFS Cf. A001792 (determinant of M(n)), A307783. Cf. A202038, A336114, A336286, A336400, A338456. Cf. A356481, A356483, A356484. Sequence in context: A283534 A294704 A264114 * A201622 A220809 A221023 Adjacent sequences: A356479 A356480 A356481 * A356483 A356484 A356485 KEYWORD nonn,hard,more AUTHOR Stefano Spezia, Aug 09 2022 STATUS approved

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Last modified February 4 05:49 EST 2023. Contains 360046 sequences. (Running on oeis4.)