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A075525 Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = ((1+t)*(1+t^2)*(1+t^3)...)^u. 2

%I

%S 1,1,1,8,3,1,6,35,6,1,144,110,95,10,1,480,1594,585,205,15,1,5760,8064,

%T 8974,1995,385,21,1,5040,125292,70252,35329,5320,658,28,1,524160,

%U 684144,1178540,392364,110649,12096,1050,36,1,2177280,14215536

%N Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = ((1+t)*(1+t^2)*(1+t^3)...)^u.

%C Also the Bell transform of A265024. For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 26 2016

%F Row sums give n!*A000009(n).

%e 1; 1,1; 8,3,1; 6,35,6,1; 144,110,95,10,1;...

%p # Adds (1,0,0,0,...) as row 0.

%p seq(PolynomialTools[CoefficientList](n!*coeff(series(mul((1+z^k)^u, k=1..20),z,20),z,n),u), n=0..9); # _Peter Luschny_, Jan 26 2016

%o (Sage)

%o # The function bell_matrix is defined in A264428.

%o # Adds (1,0,0,0,..) as row 0.

%o d = lambda n: sum((-1)^(d+1)*n/d for d in divisors(n))

%o bell_matrix(lambda n: factorial(n)*d(n+1), 9) # _Peter Luschny_, Jan 26 2016

%Y Cf. A008298.

%K nonn,tabl

%O 1,4

%A _Vladeta Jovovic_, Oct 11 2002

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Last modified February 23 08:18 EST 2019. Contains 320420 sequences. (Running on oeis4.)