通用公式:A(x,y)=x+x^2*(2*y)+x^3*(3+3*y^2)+x^4*(1+12*y+4*y^3 ^5+8*y^7)+x^9*(127+1260*y^2+1260*y ^4+252*y ^6+9*y ^8)+x^10*(1280*y+4210*y ^3+2520*y ^5+360*y ^7+10*y ^9)+x^11*(462+6930*y^2+1150*y^4+4620*y ^6+495*y ^8+11*y ^10)+x^12*(15+5548*y+60*y ^2+27720*y ^3+15*y ^4+27720*y ^5+7920*y^7+660*y^9+12*y ^11)+。。。
这样的话
求和{m>=0}(x^m+y+1/x^m)^m=A(x,y)+A(1/x,y)+(无穷大)*x^0。
在g.f.A(x,y)中,x^n*y^k,n>=1,k=0..n-1的系数T(n,k)三角形开始于:
1;
0, 2;
3, 0, 3;
1, 12, 0, 4;
10, 0, 30, 0, 5;
0, 63, 0, 60, 0, 6;
35, 0, 210, 0, 105, 0, 7;
4, 280, 6, 560, 0, 168, 0, 8;
127, 0, 1260, 0, 1260, 0, 252, 0, 9;
0, 1280, 0, 4210, 0, 2520, 0, 360, 0, 10;
462, 0, 6930, 0, 11550, 0, 4620, 0, 495, 0, 11;
15, 5548, 60, 27720, 15, 27720, 0, 7920, 0, 660, 0, 12;
1716, 0, 36036, 0, 90090, 0, 60060, 0, 12870, 0, 858, 0, 13;
0, 24129, 0, 168308, 0, 252273, 0, 120120, 0, 20020, 0, 1092, 0, 14;
6440, 0, 180190, 0, 630630, 0, 630630, 0, 225225, 0, 30030, 0, 1365, 0, 15;
57, 102960, 420, 960960, 280, 2018016, 28, 1441440, 0, 400400, 0, 43680, 0, 1680, 0, 16;
24310, 0, 875160, 0, 4084080, 0, 5717712, 0, 3063060, 0, 680680, 0, 61880, 0, 2040, 0, 17;
0, 438114, 0, 5252240, 0, 14703192, 0, 14702724, 0, 6126120, 0, 1113840, 0, 85680, 0, 2448, 0, 18;
92378, 0, 4157010, 0, 24942060, 0, 46558512, 0, 34918884, 0, 11639628, 0, 1763580, 0, 116280, 0, 2907, 0, 19;
210, 1847565, 2520, 27713400, 3150, 99768240, 840, 133024320, 45, 77597520, 0, 21162960, 0, 2713200, 0, 155040, 0, 3420, 0, 20;
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