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 A038155 a(n) = (n!/2) * Sum_{k=0..n-2} 1/k!. 12
 0, 0, 1, 6, 30, 160, 975, 6846, 54796, 493200, 4932045, 54252550, 651030666, 8463398736, 118487582395, 1777313736030, 28437019776600, 483429336202336, 8701728051642201, 165332832981201990, 3306656659624039990, 69439789852104840000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS For n>=2, a(n) gives the operation count to create all permutations of n distinct elements using Algorithm L (lexicographic permutation generation) from Knuth's The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives the number of comparisons required to find the first interchangeable element in step L3 (see answer to exercise 5). - Hugo Pfoertner, Jan 27 2003 a(n) mod 5 = A011658(n+1). - G. C. Greubel, Apr 13 2016 a(450) has 1001 decimal digits. - Michael De Vlieger, Apr 13 2016 Also the number of (undirected) paths in the complete graph K_n. - Eric W. Weisstein, Jun 04 2017 REFERENCES D. E. Knuth: The Art of Computer Programming, Volume 4, Combinatorial Algorithms, Volume 4A, Enumeration and Backtracking. Pre-fascicle 2B, A draft of section 7.2.1.2: Generating all permutations. Available online; see link. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..449 Eric Weisstein's World of Mathematics, Complete Graph Eric Weisstein's World of Mathematics, Graph Path FORMULA a(n) = 1/2*floor(n!*exp(1)-n-1), n>0. - Vladeta Jovovic, Aug 18 2002 E.g.f.: x^2/2*exp(x)/(1-x). - Vladeta Jovovic, Aug 25 2002 a(n) = Sum_{k=0..n-1} a(n-1) + k, a(0)=0. - Ilya Gutkovskiy, Apr 13 2016 a(n) = A038154(n)/2. - Alois P. Heinz, Jan 26 2017 MAPLE A038155:=n->(n!/2)*add(1/k!, k=0..n-2): seq(A038155(n), n=0..30); # Wesley Ivan Hurt, Apr 16 2016 MATHEMATICA RecurrenceTable[{a[0] == 0, a[n] == Sum[a[n - 1] + k, {k, 0, n - 1}]}, a, {n, 21}] (* Ilya Gutkovskiy, Apr 13 2016 *) Table[(n!/2) Sum[1/k!, {k, 0, n - 2}], {n, 0, 21}] (* Michael De Vlieger, Apr 13 2016 *) Table[1/2 E (n - 1) n Gamma[n - 1, 1], {n, 0, 20}] (* Eric W. Weisstein, Jun 04 2017 *) Table[If[n == 0, 0, Floor[n! E - n - 1]/2], {n, 0, 20}] (* Eric W. Weisstein, Jun 04 2017 *) CROSSREFS Cf. A011658, A038154, A038156, A056542, A079752, A079884, A080047, A080048, A080049. Sequence in context: A280474 A208790 A026112 * A026331 A135490 A345887 Adjacent sequences:  A038152 A038153 A038154 * A038156 A038157 A038158 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)