A135881 Column 0 of triangle A135880.
1, 1, 2, 6, 25, 138, 970, 8390, 86796, 1049546, 14563135, 228448504, 4002300038, 77523038603, 1646131568618, 38043008887356, 950967024783228, 25573831547118764, 736404945614783668, 22611026430036582671
Offset: 0
Keywords
Examples
Equals column 0 of triangle P=A135880: 1; 1, 1; 2, 2, 1; 6, 7, 3, 1; 25, 34, 15, 4, 1; 138, 215, 99, 26, 5, 1; 970, 1698, 814, 216, 40, 6, 1; 8390, 16220, 8057, 2171, 400, 57, 7, 1; ... where column k of P^2 equals column 0 of P^(2k+2) such that column 0 of P^2 equals this sequence shift left. Also equals column 0 of irregular triangle A135879: 1; 1,1; 2,2,1,1; 6,6,4,4,2,2,1; 25,25,19,19,13,13,9,5,5,3,1,1; 138,138,113,113,88,88,69,50,50,37,24,24,15,10,5,5,2,1; ... which has a recurrence similar to that of triangle A135877 which generates the double factorials.
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..100
Programs
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PARI
/* Generated as column 0 in triangle A135880: */ {a(n)=local(P=Mat(1),R,PShR);if(n==0,1,for(i=0,n, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));R=P*PShR; R=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,R[r,c],if(c==1,(P^2)[ #P,1],(P^(2*c-1))[r-c+1,1])))); P=matrix(#R, #R, r,c, if(r>=c, if(r<#R,P[r,c], (R^c)[r-c+1,1]))));P[n+1,1])}
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PARI
/* Generated as column 0 in triangle A135879 (faster): */ {a(n)=local(A=[1],B);if(n>0,for(i=1,n,m=1;B=[]; for(j=1,#A,if(j+m-1==floor((m+2)^2/4)-1,m+=1;B=concat(B,0));B=concat(B,A[ j])); A=Vec(Polrev(Vec(Pol(B)/(1-x+O(x^#B)))))));A[1]}
Extensions
Typo in entries (false comma) corrected by N. J. A. Sloane, Jan 23 2008
Comments