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A239840
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Number of ordered pairs of permutation functions (f,g) on n elements satisfying f(x) = f(g(g(x))).
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2
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1, 1, 4, 24, 240, 3120, 54720, 1169280, 30804480, 950745600, 34459084800, 1424870092800, 67133032243200, 3540086232883200, 208397961547776000, 13533822947893248000, 966773828738285568000, 75334352557782269952000, 6385175803136642383872000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n*a(n-1) + n*(n-1)^2*a(n-2) for n>=2, a(0) = a(1) = 1. (End)
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x + x^2 / 2). - Ilya Gutkovskiy, Jul 15 2021
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MAPLE
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a:= proc(n) a(n):= `if`(n<2, 1, n*a(n-1) +n*(n-1)^2*a(n-2)) end:
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MATHEMATICA
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a[n_] := a[n] = n a[n-1] + n(n-1)^2 a[n-2]; a[0] = a[1] = 1;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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