0,5

A071207 describes the transform of a sequence B that results in a sequence D defined by: "d(n) = the (n+1)-th term of the n-th binomial transform of sequence B". Then d(n)=sum(k=0..n, A071207(n,k)*b(k)) for n>=0, where A071207(n,k)=n^(n-k)*C(n,k). The matrix inverse of A071207 describes the inverse transform that yields B from D: b(n)=sum(k=0..n,T(n,k)*d(k)) for n>=0, where T(0,0)=1, T(n,k)=(-1)^(n-k)*C(n,k)*n*k^(n-k-1) for 0<k<=n.

T(n, k)=(-1)^(n-k)*C(n, k)*n*k^(n-k-1) for 0<k<=n, with T(0, 0)=1. O.g.f.: A(x, y)=(1-y)*sum_{n>=0}x^n*y^n/(1+n*y)^(n+2).

E.g.f. (1-y)*exp(x*y*exp(-y)) - Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 18 2003

Rows begin:

{1},

{-1,1},

{0,-4,1},

{0,9,-9,1},

{0,-16,48,-16,1},

{0,25,-200,150,-25,1},

{0,-36,720,-1080,360,-36,1},

{0,49,-2352,6615,-3920,735,-49,1},

{0,-64,7168,-36288,35840,-11200,1344,-64,1},

(PARI) T(n, k)=if(k<0|k>n, 0, if(n==0&k==0, 1, (-1)^(n-k)*binomial(n, k)*n*k^(n-k-1)))

Cf. A071207.

Sequence in context: A050465 A134575 A095831 this_sequence A127155 A048516 A060638

Adjacent sequences: A089959 A089960 A089961 this_sequence A089963 A089964 A089965

sign,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 17 2003