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 A118351 Central terms of pendular triangle A118350. 5
 1, 1, 6, 42, 325, 2688, 23286, 208659, 1918314, 17994264, 171542460, 1657212768, 16188521454, 159634359415, 1586932321578, 15886925400954, 160026976985205, 1620715748715648, 16493797802077032, 168583560794745684 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 FORMULA G.f. A=A(x) satisfies: A = 1 - 3*x*A + 3*x*A^2 + x*A^3. G.f.: 1 + Series_Reversion( x/((1+x)*(1+5*x+x^2)) ). G.f.: (1/x)*Series_Reversion( x*(1-3*x+sqrt((1-3*x)*(1-7*x)))/2/(1-3*x) ). For n>0: a(n) = 1/n*sum(j=0..n, C(n,j) *sum(i=0..(n-1), C(j,i)*C(n-j,2*j-n-i-1) *6^(2*n-3*j+2*i+1))). - Vladimir Kruchinin, Dec 26 2010 a(n) ~ s^(3/2) / (3*sqrt(2*Pi*(1 + 3*s + 3*s^2)) * n^(3/2) * r^(n+1)), where s = 2*sin(Pi/6 + arctan(sqrt(7)/3)/3) - 1, r = 2*s/(9 - 12*sin(Pi/6 - 2*arctan(sqrt(7)/3)/3)). - Vaclav Kotesovec, Feb 18 2021 MATHEMATICA T[n_, k_, p_]:= T[n, k, p] = If[n = PowerSeriesRing(ZZ, prec) return P( (x/((1+x)*(1+5*x+x^2))).reverse() ).list() a=S_list(31); [1]+a[1:] # G. C. Greubel, Feb 18 2021 (Magma) R:=PowerSeriesRing(Rationals(), 30); [1] cat Coefficients(R!( Reversion( x/((1+x)*(1+5*x+x^2)) ) )); // G. C. Greubel, Feb 18 2021 CROSSREFS Cf. A118350, A118352, A118353, A118354. Sequence in context: A145301 A107266 A142985 * A033296 A364437 A218755 Adjacent sequences: A118348 A118349 A118350 * A118352 A118353 A118354 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 26 2006 STATUS approved

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Last modified September 8 15:35 EDT 2024. Contains 375753 sequences. (Running on oeis4.)