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A248345 Signed version of A094953. 3

%I

%S 1,-1,2,2,-4,3,-2,8,-9,4,3,-12,21,-16,5,-3,18,-39,44,-25,6,4,-24,66,

%T -96,80,-36,7,-4,32,-102,184,-200,132,-49,8,5,-40,150,-320,430,-372,

%U 203,-64,9,-5,50,-210,520,-830,888,-637,296,-81,10,6,-60,285,-800,1480,-1884,1673,-1024,414,-100,11

%N Signed version of A094953.

%C This is the transformation of the polynomial 1 + 2x + 3x^2 + 4x^3 + ... + n*x^(n-1)+(n+1)*x^n to the polynomial A_0*(x+1)^0 + A_1*(x+1)^1 + A_2*(x+1)^2 + ... + A_n*(x+1)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.

%F Rows sum to 1.

%F T(n,n) = n for n >= 0.

%F T(n,n-1) = -n^2 for n >= 1.

%F T(n,2) = A007518(n)*(-1)^n for n >= 2.

%F T(n,1) = A007590(n+1)*(-1)^(n+1) for n >= 1.

%F T(n,0) = A001057(n+1) for n >= 0.

%e 1;

%e -1, 2;

%e 2, -4, 3;

%e -2, 8, -9, 4;

%e 3, -12, 21, -16, 5;

%e -3, 18, -39, 44, -25, 6;

%e 4, -24, 66, -96, 80, -36, 7;

%e -4, 32, -102, 184, -200, 132, -49, 8;

%e 5, -40, 150, -320, 430, -372, 203, -64, 9;

%e -5, 50, -210, 520, -830, 888, -637, 296, -81, 10

%o (PARI) T(n,k)=(k+1)*sum(i=0,n-k,(-1)^i*binomial(i+k+1,k+1))

%o for(n=0,15,for(k=0,n,print1(T(n,k),", ")))

%Y Cf. A007518, A007590, A001057, A094953.

%K sign,tabl,easy

%O 0,3

%A _Derek Orr_, Oct 30 2014

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Last modified October 19 03:24 EDT 2019. Contains 328211 sequences. (Running on oeis4.)