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 A186185 Expansion of 1/(1 - x*A001764(x/(1-x))/(1-x)). 0
 1, 1, 3, 11, 48, 239, 1306, 7612, 46436, 292875, 1894365, 12496864, 83753165, 568628232, 3902600850, 27031069848, 188709211952, 1326456525471, 9379857716098, 66680723764051, 476269444919163, 3416178576731504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..21. Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021. Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013. FORMULA a(n) = Sum_{m=1..n} Sum_{k=m..n} binomial(n-1,k-1)*m/(2*k-m)*binomial(3*k-2*m-1,k-m), n>0, a(0)=1. EXAMPLE G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 48*x^4 + 239*x^5 + ... The g.f. of A001764, where A001764(x) = 1 + x*A001764(x)^3, begins: A001764(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + ... The g.f. of the binomial transform of A001764 begins: A001764(x/(1-x))/(1-x) = 1 + 2*x + 6*x^2 + 25*x^3 + 126*x^4 + 704*x^5 + ... where A(x) = 1/(1 - x*A001764(x/(1-x))/(1-x)). PROG (PARI) {a(n)=if(n<0, 0, if(n==0, 1, sum(m=1, n, sum(k=m, n, binomial(n-1, k-1)*binomial(3*k-2*m-1, k-m)*m/(2*k-m)))))} (PARI) {a(n)=local(A001764=sum(m=0, n, binomial(3*m, m)*x^m/(2*m+1))+O(x^n)); polcoeff(1/(1-x*subst(A001764, x, x/(1-x))/(1-x)), n)} CROSSREFS Sequence in context: A192399 A233162 A345341 * A367874 A317170 A127087 Adjacent sequences: A186182 A186183 A186184 * A186186 A186187 A186188 KEYWORD nonn AUTHOR Vladimir Kruchinin, Feb 14 2011 STATUS approved

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Last modified February 26 02:39 EST 2024. Contains 370335 sequences. (Running on oeis4.)