#来自在线整数序列百科全书的问候!搜索:id:a36087 展示1-1-1的1 %I a336087;%S a336087 0,1,1,0,0,0,1,0,0,2,1,0,0,2,1,0,0,0,2,1,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,48,16,3,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,18,3,1,0,0,0,0719239,44,7,1,0, %U a336087 0,0,0,0,01842622117,19,3,1,0,0,0,0,0,047661607299,46,7,1,0,0,0,0,0,0124864235793,124 %N A336087按行读取的三角形:T(N,k)是具有N个(未标记)节点的森林数和k个已种植的树。 %C A336087具有N个节点的植树数等于具有N个节点的有根树的数量。[见Palmer Schwenk link,第115页]。 %H A336087 E.M.Palmer和A.J.Schwenk,关于随机森林中的树数,J.科布林。理论,B 27(1979),109-121。 %H A336087与根树相关的序列的索引项%F A336087 T(1,1)=0,如果n>=2t(n,k)=和{P_1(n,k)}(乘积{j=2..n}二项式(a00081(j-1)+c_j-1,c_j)),其中P_1(n,k)是n的k个部分大于1的分区集:2*c_2+。。。+n*n*c_n=n;c_2,…,c n>=0。;%F A336087如果k>地板(n/2),T(n,k)=0;否则T(n,n,k)=a03185(n-k,k,k)。10;%e A336087三角形T(n,k);e A336087三角T(n,k);%e A336087 n\k 1 2 2 3 4 4 5 5 6 7 8 9 10 11 11 12 13 14 15;%e A336087 1 1 0;;%e A336087 2 1 1,0;0;;%e A336087 3 3 1,0,0,0;;%e%e A336087 3 1,0,0,0;;;%e A336087,0,k e A336087 4 2,(1)0,0,0;0;;%e A336087 5 4,1,1,0,0,0;0;;%e A336087 6 9,3,1,1,0,0,0,0;;%e A336087 7 7 20,6,6,1,0,0,0,0,0,0;0;;;%e A336087 8 8 48,16,16,3,1,1,0,0,0,0,0,0,0;0;;%e的A336087 9 9 115,37,37,7,1,0,0,0,0,0,0,0;;%e的A336087 10 286,96,96,18,3,3,1,0,0,0,0,0,0,0,0,0,0,0,0 %e A336087 11 719,239,44,7,7,1,0,0,0,0,0,0,0,0,0,0;0;;%e A336087 12 1842,622,117,19,3,1,0,0,0,0,0,0,0,0,0,0,0,0,1607,299,46,7,7,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0;10;(10;(10;(;(10;(;(10;(10%e A336087 15 32973,32973,11185,11185,11185,0,0,0,0,0,0,0;0;(10 2095、320、47、7、1、0、0、0、0、0、0; %e A336087;%e A336087 n\k 1 2 3 3 4 5 6 7 8 9 10 11 11 12 13 14 15;%e A336087 A005199(6)=总和{k=1..6}(k*T(6,k))=1*9+2*2*3+3*1*1=18。;%o A336087(PARI)g(m)={my(f);如果(m==0,返回(1));f=矢量(m+1);f[1]=1;1;;%o A336087为(j=1,m,f[j+j+1,f[j+j+j+1+j+j+1,m[j[j+j+j+j=1,m,f[j[j(j=1,m,f[j=1]=1/j*和(k=1,j,sumdiv(k,d,d*f[d])*f[j-k+1]);f[m+1]};%o A336087全球(max U n=130);A000081=矢量(max U n,n,g(n-1));10;%o A336087 F(n,t)={my(s=0,D,D,c,P U 1);若(n==1,返回(0));forpart(P U 1=n,D=Set(P U 1=1,D=Set(P U 1);c=矢量(#D);对于(k=1,D#D,c[k]=#选择(x->x==D[k[k),Vec(P#=x==D[k),Vec(P P#=x==D[k,k),Vec U 1)); %o A336087 s+=产品(k=1,#D,二项式(A000081[D[k]-1]+c[k]-1,c[k]),[2,n],[t,t]);s}; %Y A336087,参见A000081,A005199,A005198(行总和),A033185。 %K A336087 nonn,表 %O A336087 1,7 %A A336087 %U Washington Bomfim_,2020年7月8日 %K A336087 NON,tabl %O A336087 1,7 %A A3360