出生日期:A(x)=1+3*x+26*x^2+429*x^3+11140*x^4+413575*x^5+20732442*x^6+1349324599*x^7+110687183288*x^8+11178507440925*x^9+。。。
定义说明。
系数表x^k/k!在exp(n*x*A(x))*(n+3-A(x)
n=0:[2,-3,-52,-2574,-267360,-49629000,-14927358240,…];
n=1:[3,0,-37,-2268,-248745,-47203552,-14374490745,…];
n=2:[4,5,0,-1462,-202352,-41536632,-13142258240,…];
n=3:[5,12,65,0,-121911,-32155140,-11164894659,…];
n=4:[6,21,164,2298,0,-18516616,-836990496,…];
n=5:[7,32,303,5636,172075,0,-4677722165,…];
n=6:[8,45,488,10242,404400,24104328,0,…];
n=7:[9,60,725,16368,708573,54605228,5760470145,0,…]。。。
其中主对角线在初始项后全部为零,说明了当n>0时,[x^n]exp(n*x*A(x))*(n+3-A(x)。
相关系列。
exp(x*A(x))=1+x+7*x^2/2!+175*x^3/3!+11065*x^4/4!+1399801*x^5/5!+307183471*x^6/6!+106838020087*x ^ 7/7!+55316481920785*x^8/8!+。。。
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