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例子
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g.f.A(x,y)中系数的三角形开始于:
1;
0, 1;
0, 2, 2;
0, 9, 14, 5;
0, 64, 124, 74, 14;
0, 624, 1388, 1074, 352, 42;
0, 7736, 18964, 17292, 7520, 1588, 132;
0, 116416, 307088, 314356, 163728, 46561, 6946, 429;
0, 2060808, 5760704, 6434394, 3807910, 1311172, 266116, 29786, 1430;
0, 41952600, 122980872, 147159406, 95921164, 37846790, 9373620, 1438006, 126008, 4862;
0, 965497440, 2945806672, 3729264888, 2623904244, 1147995184, 327833296, 61731036, 7455440, 527900, 16796;
0, 24786054816, 78270032288, 103887986400, 77816220888, 36954748286, 11761455804, 2565654006, 382043344, 37445610, 2195580, 58786; ...
其中g.f.A(x,y)=1+x*y*A(x、y+1)^2开始于:
A(x,y)=1+x*(y)+x^2*(2*y+2*y^2)+
x^3*(9*y+14*y^2+5*y^3)+
x^4*(64*y+124*y^2+74*y^3+14*y^4)+
x^5*(624*y+1388*y^2+1074*y^3+352*y^4+42*y^5)+
x^6*(7736*y+18964*y^2+17292*y^3+7520*y^4+1588*y^5+132*y^6)+
x^7*(116416*y+307088*y^2+314356*y^3+163728*y*4+46561*y^5+6946*y^6+429*y^7)+
x^8*(2060808*y+5760704*y^2+6434394*y^3+3807910*y^4+1311172*y^5+266116*y^6+29786*y^7+1430*y^8)+。。。
相关三角形。
A(x,y+1)中系数的三角形T1开始于:
1;
1,1;
4, 6, 2;
28, 52, 29, 5;
276, 590, 430, 130, 14;
3480, 8240, 7142, 2902, 562, 42;
53232, 136352, 133820, 65892, 17440, 2380, 132;
955524, 2606056, 2811333, 1588813, 515738, 97246, 9949, 429;
19672320, 56489536, 65680352, 41222664, 15498120, 3613454, 514658, 41226, 1430;
456803328, 1369670752, 1692959656, 1154579428, 485522796, 131955696, 23376294, 2621102, 169766, 4862;
11810032896, 36744177952, 47799342376, 34885949644, 16033889224, 4899599348, 1016573628, 142394476, 12962360, 695860, 16796; ...
[1, 2, 12, 114, 1440, 22368, 409248, 8585088, ...]
哪里
A(x,y+1)=1+x*(1+y)+x^2*(4+6*y+2*y^2)+
x^3*(28+52*y+29*y^2+5*y^3)+
x ^4*(276+590*y+430*y ^2+130*y ^3+14*y ^4)+
x^5*(3480+8240*y+7142*y^2+2902*y^3+562*y^4+42*y^5)+
x^6*(53232+136352*y+133820*y^2+65892*y^3+17440*y^4+2380*y^5+132*y^6)+
x^7*(955524+2606056*y+2811333*y^2+1588813*y^3+515738*y^4+97246*y^5+9949*y^6+429*y^7)+。。。
A(x,y)^2中系数的三角形T2开始于:
1;
0, 2;
0, 4, 5;
0, 18, 32, 14;
0, 128, 270, 184, 42;
0, 1248, 2940, 2488, 928, 132;
0, 15472, 39513, 38364, 18266, 4372, 429;
0, 232832, 633296, 678712, 377332, 117430, 19776, 1430;
0, 4121616, 11800512, 13648092, 8478840, 3119480, 692086, 87112, 4862;
0, 83905200, 250768144, 308424612, 208690548, 86565216, 22913292, 3836896, 376736, 16796;
0, 1930994880, 5987236848, 7750642944, 5617656996, 2555316840, 767744018, 154465024, 20330760, 1607720, 58786; ...
[1, 2, 9, 64, 624, 7736, 116416, 2060808, 41952600, ...]
哪里
A(x,y)^2=1+x*(2*y)+x^2*(4*y+5*y^2)+
x^3*(18*y+32*y^2+14*y^3)+
x^4*(128*y+270*y^2+184*y^3+42*y^4)+
x^5*(1248*y+2940*y^2+2488*y^3+928*y|4+132*y^5)+
x^6*(15472*y+39513*y^2+338364*y^3+18266*y^4+4372*y^5+429*y^6)+
x^7*(232832*y+633296*y^2+678712*y^3+377332*y^4+117430*y^5+19776*y^6+1430*y^7)+。。。
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