

A109153


Column 0 of triangle A109152.


5



1, 1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622, 6117166765086366, 60028033370994386
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OFFSET

0,3


COMMENTS

Triangular matrix T=A109152 satisfies: T(n,k) = [T^2](n1,k) for n>k+1>=1, with T(n,n) = 1 and T(n+1,n) = n+1 for n>=0.


LINKS



FORMULA

T^(m+1) = SHIFT_UP(T^m  T^(m1))  D*T^(m1) for all m where diagonal matrix D = [0, 1, 2, 3, ...] and SHIFT_UP shifts each column up 1 row.


PROG

(PARI) {a(n)=local(M=matrix(n+1, n+1)); M=M^0; for(i=1, n, M=matrix(n+1, n+1, r, c, if(r>=c, if(r==c, 1, if(r==c+1, c, (M^2)[r1, c]))))); return(M[n+1, 1])}


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



