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 A349277 Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) is the number of permutations p of [n] such that Sum_{j=1..n} j/p(j) is an integer and p(n) = k. 2
 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 8, 4, 4, 2, 2, 0, 2, 0, 8, 18, 18, 14, 18, 0, 14, 0, 0, 22, 113, 130, 102, 135, 108, 122, 0, 314, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1128, 1152, 1166, 1130, 1078, 1334, 1182, 0, 1734, 3390, 1226, 0, 1128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14520 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,15 LINKS Table of n, a(n) for n=1..91. FORMULA If n is prime, T(n,k) = 0 for 1 <= k <= n-1. T(n,n) = A073090(n-1). EXAMPLE Triangle begins: 1; 0, 1; 0, 0, 1; 1, 0, 0, 1; 0, 0, 0, 0, 2; 1, 1, 2, 2, 0, 2; 0, 0, 0, 0, 0, 0, 8; 4, 4, 2, 2, 0, 2, 0, 8; 18, 18, 14, 18, 0, 14, 0, 0, 22; 113, 130, 102, 135, 108, 122, 0, 314, 0, 104; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1128; PROG (Ruby) def A(n) ary = Array.new(n, 0) (1..n).to_a.permutation{|i| ary[i[-1] - 1] += 1 if (1..n).inject(0){|s, j| s + j / i[j - 1].to_r}.denominator == 1 } ary end def A349277(n) (1..n).map{|i| A(i)}.flatten end p A349277(8) CROSSREFS Row sum gives A073090. Sequence in context: A034798 A225803 A357458 * A307014 A240871 A236765 Adjacent sequences: A349274 A349275 A349276 * A349278 A349279 A349280 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Nov 12 2021 STATUS approved

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Last modified August 10 16:53 EDT 2024. Contains 375058 sequences. (Running on oeis4.)