The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A171694 Expansion generating function using an infinite sum:m=-2; f(t,y)=Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m*t])*y^x, {x, 0, Infinity}] 1
 1, 2, 2, 6, 20, 6, 26, 154, 190, 14, 150, 1160, 3428, 1352, 54, 1082, 9174, 50404, 51724, 10434, 62, 9366, 78476, 683962, 1376232, 734122, 65996, 966, 94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786, 1091670, 7562000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are: {1, 4, 32, 384, 6144, 122880, 2949120, 82575360, 2642411520, 95126814720, 3805072588800,...}. 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^(2*n)*n! EXAMPLE {1}, {2, 2}, {6, 20, 6}, {26, 154, 190, 14}, {150, 1160, 3428, 1352, 54}, {1082, 9174, 50404, 51724, 10434, 62}, {9366, 78476, 683962, 1376232, 734122, 65996, 966}, {94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786}, {1091670, 7562000, 122859048, 611454960, 1132022084, 653476464, 111158184, 2715536, 71574}, {14174522, 84743566, 1725925480, 11633772184, 33628718668, 34398480388, 12391430344, 1218784120, 31661386, -875938}, {204495126, 1021304852, 25642306094, 216329822576, 907078630988, 1476556625528, 949722706028, 213543053936, 14943309854, 17523092, 12810726} MATHEMATICA Clear[m, n, t, x, y, a] m = -2; 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^(2*n)*n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 0, 10}] Flatten[a] CROSSREFS Sequence in context: A176754 A173098 A233113 * A103179 A320932 A225942 Adjacent sequences:  A171691 A171692 A171693 * A171695 A171696 A171697 KEYWORD sign,uned AUTHOR Roger L. Bagula, Dec 15 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)