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Search: id:A154923
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| A154923 |
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A symmetrical triangle sequence made from A154537:q(x,n)= Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]); p(x,n)=q(x,n)+x^n*q(1/x,n); t(n,m)=coefficients(p(x,n)). |
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| 2, 3, 3, 5, 16, 5, 9, 62, 62, 9, 17, 208, 464, 208, 17, 33, 642, 2680, 2680, 642, 33, 65, 1880, 13404, 24320, 13404, 1880, 65, 129, 5322, 62188, 180488, 180488, 62188, 5322, 129, 257, 14752, 280144, 1209600, 1858752, 1209600, 280144, 14752, 257, 513
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:
{2, 6, 26, 142, 914, 6710, 55018, 496254, 4868258, 51483878, 582795578,...}
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FORMULA
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q(x,n)= Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]);
p(x,n)=q(x,n)+x^n*q(1/x,n);
t(n,m)=coefficients(p(x,n)).
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EXAMPLE
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{2},
{3, 3},
{5, 16, 5},
{9, 62, 62, 9},
{17, 208, 464, 208, 17},
{33, 642, 2680, 2680, 642, 33},
{65, 1880, 13404, 24320, 13404, 1880, 65},
{129, 5322, 62188, 180488, 180488, 62188, 5322, 129},
{257, 14752, 280144, 1209600, 1858752, 1209600, 280144, 14752, 257},
{513, 40418, 1262544, 7828640, 16609824, 16609824, 7828640, 1262544, 40418, 513},
{1025, 110248, 5787604, 50950400, 140957728, 187181568, 140957728, 50950400, 5787604, 110248, 1025}
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MATHEMATICA
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p[x_, n_] = Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]);
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}]'
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]
+ Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}]'
Flatten[%]
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CROSSREFS
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A154537
Sequence in context: A064339 A053199 A045626 this_sequence A154693 A065854 A064776
Adjacent sequences: A154920 A154921 A154922 this_sequence A154924 A154925 A154926
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KEYWORD
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nonn,tabl,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 17 2009
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