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 A171693 Expansion generating function using an infinite sum odd levels:m=0; f(t,y)=Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m*t])*y^x, {x, 0, Infinity}] 2
 1, -1, 14, -1, 4, -16, 504, -16, 4, -34, 372, 2178, 35288, 2178, 372, -34, 496, -5888, 65728, 749824, 4185760, 749824, 65728, -5888, 496, -11056, 154912, -767856, 23350656, 230640288, 770603712, 230640288, 23350656, -767856, 154912, -11056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS Row sums are: {1, 12, 480, 40320, 5806080, 1277337600,...}. m=-1 gives MacMahon {1,6,1} A060187. LINKS FORMULA Infinite sum on an generalized Euler numbers/ polynomial scaled generating function: f(t,y)=Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m*t])*y^x, {x, 0, Infinity}] Scaling function is: g(y,n)=((1 - y)^(n + 1)*2^(1 + Floor[(n)/2])/(1 + y))*n! EXAMPLE {1}, {-1, 14, -1}, {4, -16, 504, -16, 4}, {-34, 372, 2178, 35288, 2178, 372, -34}, {496, -5888, 65728, 749824, 4185760, 749824, 65728, -5888, 496}, {-11056, 154912, -767856, 23350656, 230640288, 770603712, 230640288, 23350656, -767856, 154912, -11056} MATHEMATICA Clear[m, n, t, x, y, a] m = 0; f[t_, y_] = Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m* t])*y^x, {x, 0, Infinity}] a = Table[ CoefficientList[FullSimplify[ExpandAll[((1 - y)^(n + 1)*2^(1 + Floor[(n)/2])/(1 + y))*n!* SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 1, 11, 2}] Flatten[a] CROSSREFS Sequence in context: A040204 A040203 A040205 * A235704 A229199 A040206 Adjacent sequences:  A171690 A171691 A171692 * A171694 A171695 A171696 KEYWORD sign,uned AUTHOR Roger L. Bagula, Dec 15 2009 STATUS approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)