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We say that a word is in "standard order" if it has the property that whenever a letter i appears, the letter i-1 has already appeared in the word. This implies that all words begin with the letter 1.
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Let X be the random variable that assigns to each permutation of {1,2,...,b} (with uniform distribution) its number of fixed points (as in A008290). Then T(b,n) is the n^-th moment about 0 of X, i.e., the expected value of X^n. - Geoffrey Critzer, Jun 23 2020
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Let X be the random variable that assigns to each permutation of {1,2,...,b} (with uniform distribution) its number of fixed points (as in A008290). Then T(b,n) is the n^th moment about 0 of X, i.e., the expected value of X^n. - Geoffrey Critzer, Jun 23 2020
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Andrew Howroyd, <a href="/A278984/b278984.txt">Table of n, a(n) for n = 1..1275</a>
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