cp's OEIS Frontend

A248345 Signed version of A094953.

%I A248345 #35 Nov 04 2014 22:38:44
%S A248345 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 A248345 -96,80,-36,7,-4,32,-102,184,-200,132,-49,8,5,-40,150,-320,430,-372,
%U A248345 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 A248345 Signed version of A094953.
%C A248345 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 A248345 Rows sum to 1.
%F A248345 T(n,n) = n for n >= 0.
%F A248345 T(n,n-1) = -n^2 for n >= 1.
%F A248345 T(n,2) = A007518(n)*(-1)^n for n >= 2.
%F A248345 T(n,1) = A007590(n+1)*(-1)^(n+1) for n >= 1.
%F A248345 T(n,0) = A001057(n+1) for n >= 0.
%e A248345 1;
%e A248345 -1,  2;
%e A248345 2,  -4,    3;
%e A248345 -2,  8,   -9,    4;
%e A248345 3, -12,   21,  -16,    5;
%e A248345 -3, 18,  -39,   44,  -25,    6;
%e A248345 4, -24,   66,  -96,   80,  -36,    7;
%e A248345 -4, 32, -102,  184, -200,  132,  -49,   8;
%e A248345 5, -40,  150, -320,  430, -372,  203, -64,   9;
%e A248345 -5, 50, -210,  520, -830,  888, -637, 296, -81, 10
%o A248345 (PARI) T(n,k)=(k+1)*sum(i=0,n-k,(-1)^i*binomial(i+k+1,k+1))
%o A248345 for(n=0,15,for(k=0,n,print1(T(n,k),", ")))
%Y A248345 Cf. A007518, A007590, A001057, A094953.
%K A248345 sign,tabl,easy
%O A248345 0,3
%A A248345 _Derek Orr_, Oct 30 2014