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 A001392 a(n) = 9*binomial(2n,n-4)/(n+5). (Formerly M4637 N1981) 25
 1, 9, 54, 273, 1260, 5508, 23256, 95931, 389367, 1562275, 6216210, 24582285, 96768360, 379629720, 1485507600, 5801732460, 22626756594, 88152205554, 343176898988, 1335293573130, 5193831553416, 20198233818840, 78542105700240, 305417807763705 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 COMMENTS Number of n-th generation vertices in the tree of sequences with unit increase labeled by 8 (cf. Zoran Sunic reference) - Benoit Cloitre, Oct 07 2003 Number of lattice paths from (0,0) to (n,n) with steps E=(1,0) and N=(0,1) which touch but do not cross the line x-y=4. - Herbert Kociemba, May 24 2004 Number of standard tableaux of shape (n+4,n-4). - Emeric Deutsch, May 30 2004 a(n) = A214292(2*n-1,n-5) for n > 4. - Reinhard Zumkeller, Jul 12 2012 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 4..200 R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6. A. Papoulis, A new method of inversion of the Laplace transform, Quart. Appl. Math 14 (1957), 405-414. [Annotated scan of selected pages] A. Papoulis, A new method of inversion of the Laplace transform, Quart. Applied Math. 14 (1956), 405ff. J. Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222. Zoran Sunic, Self-Describing Sequences and the Catalan Family Tree, Electronic Journal of Combinatorics, 10 (2003) #N5. FORMULA Expansion of x^4*C^9, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108. - Philippe Deléham, Feb 03 2004 Let A be the Toeplitz matrix of order n defined by: A[i,i-1]=-1, A[i,j]=Catalan(j-i), (i<=j), and A[i,j]=0, otherwise. Then, for n>=8, a(n-4)=(-1)^(n-8)*coeff(charpoly(A,x),x^8). - Milan Janjic, Jul 08 2010 D-finite with recurrence -(n+5)*(n-4)*a(n) +2*n*(2*n-1)*a(n-1)=0. - R. J. Mathar, Jun 20 2013 From Ilya Gutkovskiy, Jan 22 2017: (Start) E.g.f.: (1/24)*x^4*1F1(9/2; 10; 4*x). a(n) ~ 9*4^n/(sqrt(Pi)*n^(3/2)). (End) EXAMPLE G.f. = x^4 + 9*x^5 + 54*x^6 + 273*x^7 + 1260*x^8 + 5508*x^9 + 23256*x^10 + ... MAPLE A001392:=n->9*binomial(2*n, n-4)/(n+5): seq(A001392(n), n=4..40); # Wesley Ivan Hurt, Apr 11 2017 MATHEMATICA Table[9*Binomial[2n, n-4]/(n+5), {n, 4, 30}] (* Harvey P. Dale, Mar 03 2011 *) PROG (PARI) a(n)=9*binomial(n+n, n-4)/(n+5) \\ Charles R Greathouse IV, Jul 31 2011 CROSSREFS First differences are in A026015. A diagonal of any of the essentially equivalent arrays A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072. Cf. A000108, A000245, A002057, A000344, A003517, A000588, A003518, A003519. Sequence in context: A169796 A027472 A022637 * A188428 A243415 A276602 Adjacent sequences:  A001389 A001390 A001391 * A001393 A001394 A001395 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Harvey P. Dale, Mar 03 2011 STATUS approved

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Last modified April 22 07:02 EDT 2021. Contains 343162 sequences. (Running on oeis4.)