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 A070779 Expansion of e.g.f.: (exp(x/(1-x))*(2-x)-1+x)/(1-x)^3. 3
 1, 5, 28, 185, 1426, 12607, 125882, 1401409, 17209234, 231033431, 3365440882, 52855452817, 890097287834, 15996379554079, 305519496498106, 6178746162639617, 131885301216119842, 2962568890205560999, 69853182607494217154, 1724761580035969997521, 44501146220521229674282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equal to the number of strictly partial permutations on [n]; i.e. equal to the cardinality of the complement I_n\S_n, where I_n and S_n denote the symmetric inverse monoid and symmetric group on [n]. - James East, May 03 2007 Former name was "E.g.f.: (exp(x/(1-x))-1)/(1-x)."  However, that would be the e.g.f. with offset 1 rather than 0. - Robert Israel, Jan 03 2019 LINKS Robert Israel, Table of n, a(n) for n = 0..442 FORMULA In Maple notation, a(n) = n! *(n+1)^2 *hypergeom([1, -n], [2, 2], -1). a(n) = (n+1)!*(LaguerreL(n+1, -1)-1). - Vladeta Jovovic, Oct 24 2003 a(n) = A002720(n) - A000142(n) = Sum_{k=0..n-1} k!*binomial(n,k)^2. - James East, May 03 2007 D-finite with recurrence a(n) = (3*n+2)*a(n-1) - 3*n^2*a(n-2) + n*(n-1)^2*a(n-3). - Robert Israel, Jan 03 2019 MAPLE f:= gfun:-rectoproc({(n + 3)*(n + 2)^2*a(n) - 3*(n + 3)^2*a(n + 1) + (3*n + 11)*a(n + 2) - a(n + 3)=0, a(0)=1, a(1)=5, a(2)=28}, a(n), remember): map(f, [\$0..30]); # Robert Israel, Jan 03 2019 # alternative A070779 := proc(n)     n!*(n+1)^2*hypergeom([1, -n], [2, 2], -1) ;     simplify(%) ; end proc: # R. J. Mathar, Jul 16 2020 MATHEMATICA Table[(n + 1)! (LaguerreL[n + 1, -1] -1), {n, 0, 20}] (* Vincenzo Librandi, Jan 04 2019 *) With[{nn=20}, CoefficientList[Series[(Exp[x/(1-x)](2-x)-1+x)/(1-x)^3, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 07 2020 *) PROG (Sage) @cached_function def a(n):     if n < 3: return [1, 5, 28][n]     return n*(n-1)^2*a(n-3)-3*n^2*a(n-2)+(3*n+2)*a(n-1) [a(n) for n in (0..20)] # Peter Luschny, Jan 04 2019 CROSSREFS Cf. A002720, A000142. Sequence in context: A156629 A331797 A123776 * A189487 A024065 A003467 Adjacent sequences:  A070776 A070777 A070778 * A070780 A070781 A070782 KEYWORD nonn AUTHOR ~~Karol A. Penson, May 06 2002 EXTENSIONS New description from Vladeta Jovovic, Apr 10 2003 Edited by Robert Israel, Jan 03 2019 Definition clarified by Harvey P. Dale, Sep 07 2020 STATUS approved

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Last modified September 25 19:14 EDT 2020. Contains 337344 sequences. (Running on oeis4.)