搜索: 编号:177984
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A177984号
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| 多项式系数的对称三角形:p(x,n)=如果[n==0,1,(1-x)^(n+1)*Sum[(2*k+1)^n+(k+1)|n+k^n)*x^k,{k,0,Infinity}]/2] |
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1, 1, 1, 1, 4, 1, 1, 14, 14, 1, 1, 44, 126, 44, 1, 1, 132, 887, 887, 132, 1, 1, 390, 5451, 12076, 5451, 390, 1, 1, 1150, 30984, 131665, 131665, 30984, 1150, 1, 1, 3400, 168076, 1252600, 2353126, 1252600, 168076, 3400, 1, 1, 10088, 885725, 10905407, 34828859
(列表;桌子;图表;参考;听;历史;文本;内部格式)
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抵消
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0,5
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评论
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行总和为:
{1, 2, 6, 30, 216, 2040, 23760, 327600, 5201280, 93260160, 1861574400,...}.
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链接
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配方奶粉
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p(x,n)=如果[n==0,1,(1-x)^(n+1)*Sum[(2*k+1)^n+(k+1)m+k^n)*x^k,{k,0,无限}]/2];
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示例
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{1},
{1, 1},
{1, 4, 1},
{1, 14, 14, 1},
{1, 44, 126, 44, 1},
{1, 132, 887, 887, 132, 1},
{139054512076541390,1},
{1, 1150, 30984, 131665, 131665, 30984, 1150, 1},
{1, 3400, 168076, 1252600, 2353126, 1252600, 168076, 3400, 1},
{10088、885725、10905407、34828859、34828859、10905407、885725、10088、1},
{1, 30026, 4582497, 89401968, 454344414, 764856588, 454344414, 89401968, 4582497, 30026, 1}
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数学
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p[x_,n_]=如果[n==0,1,(1-x)^(n+1)*和[((2*k+1)^n+(k+1)^n+k^n)*x^k,{k,0,无穷大}]/2];
表[系数列表[FullSimplify[ExpandAll[p[x,n]],x],{n,0,10}];
压扁[%]
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交叉参考
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关键词
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作者
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状态
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经核准的
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