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 A120589 Self-convolution of A120588, such that a(n) = 3*A120588(n) for n>=2. 1
 1, 2, 3, 6, 15, 42, 126, 396, 1287, 4290, 14586, 50388, 176358, 624036, 2228700, 8023320, 29084535, 106073010, 388934370, 1432916100, 5301789570, 19692361260, 73398801060, 274447690920, 1029178840950, 3869712441972, 14585839204356 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n >= 2, a(n) equals 2^(2n+1) times the coefficient of pi in 2F1(3/2,n+1,5/2,-1). [John M. Campbell, Jul 17 2011] LINKS Guo-Niu Han, Enumeration of Standard Puzzles Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy] S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243, 2012. - From N. J. A. Sloane, May 09 2012 Sergey Kitaev, Jeffrey Remmel, Mark Tiefenbruck, Quadrant Marked Mesh Patterns in 132-Avoiding Permutations II, Electronic Journal of Combinatorial Number Theory, Volume 15 #A16. (arXiv:1302.2274) FORMULA a(n) = 3*A000108(n-1) for n>=2, where A000108 is the Catalan numbers. EXAMPLE A(x) = 1 + 2*x + 3*x^2 + 6*x^3 + 15*x^4 + 42*x^5 + 126*x^6 + 396*x^7 +... A(x)^(1/2) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 42*x^6 + 132*x^7 +... MATHEMATICA Join[{1, 2, 3}, Table[3*(2*n)!/n!/(n+1)!, {n, 2, 40}]] PROG (PARI) {a(n)=local(A=1+x+x^2+x*O(x^n)); for(i=0, n, A=A-3*A+2+x+A^2); polcoeff(A^2, n)} CROSSREFS Cf. A120588 (A(x)^(1/2)); A120590-A120607. Sequence in context: A129960 A115098 A036418 * A110181 A141351 A088793 Adjacent sequences:  A120586 A120587 A120588 * A120590 A120591 A120592 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 16 2006 STATUS approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)