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 A045500 Fifth-from-right diagonal of triangle A121207. 4
 1, 1, 6, 27, 125, 635, 3488, 20425, 126817, 831915, 5744784, 41618459, 315388311, 2493721645, 20526285716, 175529425815, 1556577220651, 14290644428279, 135624265589086, 1328702240382589, 13420603191219111, 139592874355534071 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS With leading 0 and offset 4: number of permutations beginning with 54321 and avoiding 1-23. - Ralf Stephan, Apr 25 2004 a(n) is the number of set partitions of {1,2,...,n+4} in which the last block has length 4: the blocks are arranged in order of their least element. - Don Knuth, Jun 12 2017 REFERENCES See also references under sequence A040027. LINKS S. Kitaev, Generalized pattern avoidance with additional restrictions, Sem. Lothar. Combinat. B48e (2003). S. Kitaev and T. Mansour, Simultaneous avoidance of generalized patterns, arXiv:math/0205182 [math.CO], 2014. FORMULA a(n+1) = Sum_{k=0..n} binomial(n+4, k+4)*a(k). - Vladeta Jovovic, Nov 10 2003 With offset 4, e.g.f.: x^4 + exp(exp(x))/24 * int[0..x, t^4*exp(-exp(t)+t) dt]. - Ralf Stephan, Apr 25 2004 O.g.f. satisfies: A(x) = 1 + x*A( x/(1-x) ) / (1-x)^5. [From Paul D. Hanna, Mar 23 2012] MATHEMATICA a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n+3, k+4]*a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 14 2018, after Vladeta Jovovic *) PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*subst(A, x, x/(1-x+x*O(x^n)))/(1-x)^5); polcoeff(A, n)} /* Paul D. Hanna, Mar 23 2012 */ (Python) # The function Gould_diag is defined in A121207. A045500_list = lambda size: Gould_diag(5, size) print(A045500_list(24)) # Peter Luschny, Apr 24 2016 CROSSREFS Cf. A040027, A045499, A045501, A121207. Column k=4 of A124496. Sequence in context: A249792 A002912 A030297 * A109115 A038176 A104745 Adjacent sequences:  A045497 A045498 A045499 * A045501 A045502 A045503 KEYWORD easy,nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Nov 10 2003 Entry revised by N. J. A. Sloane, Dec 11 2006 STATUS approved

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Last modified December 4 00:33 EST 2020. Contains 338920 sequences. (Running on oeis4.)