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A059114 Triangle T(n,m)= Sum_{i=0..n} L'(n,i)*Product_{j=1..m} (i-j+1), m=0..n. 1

%I

%S 1,1,1,3,4,2,13,21,18,6,73,136,156,96,24,501,1045,1460,1260,600,120,

%T 4051,9276,15030,16320,11160,4320,720,37633,93289,170142,219450,

%U 192360,108360,35280,5040,394353,1047376,2107448,3116736,3294480,2405760

%N Triangle T(n,m)= Sum_{i=0..n} L'(n,i)*Product_{j=1..m} (i-j+1), m=0..n.

%C L'(n,i) are unsigned Lah numbers (Cf. A008297):L'(n,i)=n!/i!*binomial(n-1,i-1) for i >= 1, L'(0,0)=1, L'(n,0)=0 for n>0.T(n,0)=A000262(n); T(n,2)=A052852(n). Row sums give A059115.

%F E.g.f. for T(n, m)=(x/(1-x))^m*e^(x/(x-1)).

%e [1], [1, 1], [3, 4, 2], [13, 21, 18, 6], [73, 136, 156, 96, 24], [501, 1045, 1460, 1260, 600, 120], ...; E.g.f. for T(n, 2) = (x/(1-x))^2*e^(x/(x-1)) = x^2 + 3*x^3 + 13/2*x^4 + 73/6*x^5 + 167/8*x^6 + 4051/120*x^7 + ...

%Y Cf. A059110, A052897.

%K easy,nonn,tabl

%O 0,4

%A _Vladeta Jovovic_, Jan 04 2001

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Last modified August 24 18:52 EDT 2019. Contains 326295 sequences. (Running on oeis4.)