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 A327873 Irregular triangle read by rows: T(n,k) is the number of length n primitive (aperiodic) palindromes using exactly k different symbols, 1 <= k <= ceiling(n/2). 8
 1, 0, 0, 2, 0, 2, 0, 6, 6, 0, 4, 6, 0, 14, 36, 24, 0, 12, 36, 24, 0, 28, 150, 240, 120, 0, 24, 144, 240, 120, 0, 62, 540, 1560, 1800, 720, 0, 54, 534, 1560, 1800, 720, 0, 126, 1806, 8400, 16800, 15120, 5040, 0, 112, 1770, 8376, 16800, 15120, 5040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..2550 FORMULA T(n,k) = Sum_{j=1..k} (-1)^(k-j)*binomial(k,j)*A284823(n,j). T(n,k) = Sum_{d|n} mu(n/d)*k!*Stirling2(ceiling(d/2), k). EXAMPLE Triangle begins:   1;   0;   0,   2;   0,   2;   0,   6,    6;   0,   4,    6;   0,  14,   36,   24;   0,  12,   36,   24;   0,  28,  150,  240,   120;   0,  24,  144,  240,   120;   0,  62,  540, 1560,  1800,   720;   0,  54,  534, 1560,  1800,   720;   0, 126, 1806, 8400, 16800, 15120, 5040;   0, 112, 1770, 8376, 16800, 15120, 5040;   ... PROG (PARI) T(n, k) = {sumdiv(n, d, moebius(n/d)*k!*stirling(ceil(d/2), k, 2))} CROSSREFS Columns k=2..6 are A056463, A056464, A056465, A056466, A056467. Row sums are A327874. Cf. A284823, A327878. Sequence in context: A136581 A175950 A066285 * A136665 A047765 A068463 Adjacent sequences:  A327870 A327871 A327872 * A327874 A327875 A327876 KEYWORD nonn,tabf AUTHOR Andrew Howroyd, Sep 28 2019 STATUS approved

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Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)