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 A046662 Sum of mistyped version of binomial coefficients. 7
 1, 2, 7, 52, 749, 17686, 614227, 29354312, 1844279257, 147273109354, 14561325802271, 1745720380045852, 249461639720702917, 41886684733511640062, 8164388189339113521259, 1828191138807263097870256, 466057478369217965809683377, 134193343258948416556377786322 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of (n!)^2. - Peter Luschny, May 31 2014 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..253 Roland Bacher, Counting Packings of Generic Subsets in Finite Groups, Electr. J. Combinatorics, 19 (2012), #P7. - From N. J. A. Sloane, Feb 06 2013 FORMULA a(n) = Sum_{k=0..n} n!*k!/(n-k)!. E.g.f.: exp(x)*F(x), with F(x) = Sum_{k>=0} k!*x^k. - Ralf Stephan, Apr 02 2004 a(n) = n^2*a(n - 1) - n*(n - 1)*a(n - 2) + 1. - Vladeta Jovovic, Jul 15 2004 From Peter Bala, Nov 26 2017: (Start) a(k) == a(0) (mod k) for all k (by the inhomogeneous recurrence equation). More generally, a(n+k) = a(n) (mod k) for all n and k (by an induction argument on n). It follows that for each positive integer k, the sequence a(n) (mod k) is periodic, with the exact period dividing k. For example, modulo 10 the sequence becomes 1, 2, 7, 2, 9, 6, 7, 2, 7, 4, 1, 2, 7, 2, 9, 6, 7, 2, 7, 4, ... with exact period 10. (End) G.f.: Sum_{k>=0} (k!)^2*x^k/(1 - x)^(k+1). - Ilya Gutkovskiy, Apr 12 2019 a(n) ~ (n!)^2. - Vaclav Kotesovec, May 03 2021 MATHEMATICA Table[Sum[(n!k!)/(n-k)!, {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Sep 29 2012 *) CROSSREFS Cf. A003149, A064570, A229464. Sequence in context: A138737 A216086 A210856 * A237195 A275597 A118191 Adjacent sequences:  A046659 A046660 A046661 * A046663 A046664 A046665 KEYWORD nonn,easy AUTHOR EXTENSIONS Corrected and extended by Harvey P. Dale, Sep 29 2012 STATUS approved

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Last modified June 25 02:36 EDT 2021. Contains 345449 sequences. (Running on oeis4.)