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 A276179 n^2 * a(n) = 2*(7*n^2 - 7*n + 3)*a(n-1) - 12*(7*n^2 - 14*n + 9)*a(n-2) + 39*(7*n^2 - 21*n + 18) * a(n-3) - 72*(7*n^2 - 28*n + 30)*a(n-4) + 72*(7*n^2 - 35*n + 45) * a(n-5) - 216*(n-3)^2 * a(n-6), with a(0)=1, a(1)=6, a(2)=24, a(3)=78, a(4)=216, a(5)=504. 2
 1, 6, 24, 78, 216, 504, 906, 756, -2808, -17832, -57312, -104832, 81882, 1734156, 9360576, 35755956, 106475472, 232967664, 215497680, -1178534304, -8734303296, -36146763648, -108833048064, -220247838720, -46688571558, 2220777704700, 13473296923536, 53523581091900 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Gheorghe Coserea, Table of n, a(n) for n = 0..301 Robert S. Maier, On Rationally Parametrized Modular Equations, arXiv:math/0611041 [math.NT], 2006. FORMULA n^2 * a(n) = 2*(7*n^2 - 7*n + 3)*a(n-1) - 12*(7*n^2 - 14*n + 9)*a(n-2) + 39*(7*n^2 - 21*n + 18) * a(n-3) - 72*(7*n^2 - 28*n + 30)*a(n-4) + 72*(7*n^2 - 35*n + 45) * a(n-5) - 216*(n-3)^2 * a(n-6), with a(0)=1, a(1)=6, a(2)=24, a(3)=78, a(4)=216, a(5)=504. 0 = x*(x+2)*(x+3)*(x^2+3*x+3)*(x^2+6*x+12)*y'' + (7*x^6 + 84*x^5 + 420*x^4 + 1092*x^3 + 1512*x^2 + 1008*x + 216)*y' + 9*(x+2)^2 * (x^3 + 6*x^2 + 12*x + 6)*y, where y(x) = A(x/-6). EXAMPLE A(x) = 1 + 6*x + 24*x^2 + 78*x^3 + 216*x^4 + 504*x^5 + 906*x^6 + ... is the g.f. PROG (PARI) seq(N) = {   my(a = vector(N));   a[1] = 6; a[2] = 24; a[3] = 78; a[4] = 216; a[5] = 504; a[6] = 906;   for (n = 7, N,   my(t1 = 2*(7*n^2 - 7*n + 3)*a[n-1] - 12*(7*n^2 - 14*n + 9)*a[n-2],      t2 = 39*(7*n^2 - 21*n + 18) * a[n-3] - 72*(7*n^2 - 28*n + 30)*a[n-4],      t3 = 72*(7*n^2 - 35*n + 45) * a[n-5] - 216*(n-3)^2 * a[n-6]);      a[n] = (t1+t2+t3)/n^2);   concat(1, a); }; seq(33) (MAGMA) I:=[6, 24, 78, 216, 504, 906]; [1] cat [n le 6 select I[n] else (2*(7*n^2-7*n+3)*Self(n-1)-12*(7*n^2-14*n+9)*Self(n-2)+39*(7*n^2-21*n+18)*Self(n-3)-72*(7*n^2-28*n+30)*Self(n-4)+72*(7*n^2-35*n+45)*Self(n-5)-216*(n-3)^2*Self(n-6)) div n^2: n in [1..30]]; // Vincenzo Librandi, Aug 25 2016 CROSSREFS Cf. A091401, A276018. Sequence in context: A341364 A080373 A180437 * A162583 A259662 A058809 Adjacent sequences:  A276176 A276177 A276178 * A276180 A276181 A276182 KEYWORD sign AUTHOR Gheorghe Coserea, Aug 24 2016 STATUS approved

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Last modified August 11 20:13 EDT 2022. Contains 356067 sequences. (Running on oeis4.)