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 A362767 Number of multisets of permutations with a combined total of n moved points spanning an initial interval of positive integers. 2
 1, 0, 1, 2, 16, 94, 836, 8062, 92434, 1187780, 17103983, 271660992, 4722454300, 89127765656, 1814841101699, 39650794527652, 925141689393748, 22957155125457704, 603681013763369997, 16767920412944383544, 490550926763623941996, 15076432260424342403648, 485630804356929583800760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 EXAMPLE In the following examples permutations are shown using cycle notation. The a(2) = 1 multiset of permutations is {(12)}. The a(3) = 2 multisets of permutations are {(123)}, {(132)}. The a(4) = 16 multisets of permutations are A000166(4) = 9 derangements plus 7 pairs of transpositions which are: {(12), (34)}, {(13), (24)}, {(14), (23)}, {(12), (13)}, {(12), (23)}, {(13), (23)}, {(12), (12)}. PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} R(k, n, b)={EulerT(vector(n, j, binomial(k, j)*polcoef(b, j)))} seq(n)={my(b=serlaplace(exp(-x + O(x*x^n))/(1-x))); concat([1], sum(k=1, n, R(k, n, b) * sum(r=k, n, binomial(r, k)*(-1)^(r-k)) ))} CROSSREFS Cf. A000166, A362768 (strict case). Sequence in context: A271273 A220882 A295903 * A141243 A163229 A038749 Adjacent sequences: A362764 A362765 A362766 * A362768 A362769 A362770 KEYWORD nonn AUTHOR Andrew Howroyd, May 04 2023 STATUS approved

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Last modified September 18 08:11 EDT 2024. Contains 375997 sequences. (Running on oeis4.)