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 A347940 Array T(n, k) = Sum_{j=2..n+2} (-1)^(n-j)*Stirling2(n+1, j-1)*j!*j^k/2, for n and k >= 0, read by antidiagonals. 0
 1, 2, 2, 4, 7, 4, 8, 23, 23, 8, 16, 73, 115, 73, 16, 32, 227, 533, 533, 227, 32, 64, 697, 2359, 3451, 2359, 697, 64, 128, 2123, 10133, 20753, 20753, 10133, 2123, 128, 256, 6433, 42655, 118843, 164731, 118843, 42655, 6433, 256, 512, 19427, 177053, 657833, 1220657, 1220657, 657833, 177053, 19427, 512 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS T(m, n) is the number of saturated Cp^m*q^n-transfer systems where Cp^m*q^n is the cyclic group of order p^m*q^n, for m, n >= 0, p and q primes. See Hafeez et al. link page 1. LINKS Table of n, a(n) for n=0..54. Arvind Ayyer and Beáta Bényi, Toppling on permutations with an extra chip, El. J. Comb., 28 (2021), P4.18. The array seems to appear in Table 6. Usman Hafeez, Peter Marcus, Kyle Ormsby and Angélica Osorno, Saturated and linear isometric transfer systems for cyclic groups of order p^m*q^n, arXiv:2109.08210 [math.AT], 2021. FORMULA T(n,k) = T(k,n). T(n,k) = Sum_{j=0..min(n,k)} (j!*(j+2)!/2)*Stirling2(n+2,j+2;2)*Stirling2(k+2,j+2;2), n,k >= 0, where Stirling2(n,k;2) are the 2-Stirling numbers of the second kind A143494. - Fabián Pereyra, Jan 08 2022 EXAMPLE Array begins: 1 2 4 8 16 32 ... 2 7 23 73 227 697 ... 4 23 115 533 2359 10133 ... 8 73 533 3451 20753 118843 ... 16 227 2359 20753 164731 1220657 ... 32 697 10133 118843 1220657 11467387 ... ... PROG (PARI) T(n, k) = sum(j=2, n+2, (-1)^(n-j)*stirling(n+1, j-1, 2)*j!*j^k/2); CROSSREFS Columns k=0-1 gives A000079, A083313(n+1). Main diagonal gives A220181(n+1). Cf. A008277 (Stirling2), A143494. Sequence in context: A300937 A300881 A301491 * A208269 A184761 A270227 Adjacent sequences: A347937 A347938 A347939 * A347941 A347942 A347943 KEYWORD nonn,tabl AUTHOR Michel Marcus, Sep 20 2021 STATUS approved

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Last modified October 4 22:44 EDT 2023. Contains 365888 sequences. (Running on oeis4.)