A101982 - OEIS

%I #5 Mar 30 2012 18:36:44

%S 0,1,3,4,11,-44,942,-23561,806955,-35956868,2023718198,-140435834681,

%T 11782131588086,-1175694615277233,137629159046661089,

%U -18679508311308283526,2909710453923000618155,-515605748075502971981108,103130355820655917046896638,-23123715029010809457898920545

%N Row sums of triangle A101980, which is the matrix logarithm of A008459 (squared entries of Pascal's triangle).

%C A101981 is essentially a signed offset version of A002190 and is related to Bessel functions.

%F a(n) = Sum_{k=0..n} A101981(n-k)*C(n, k)^2.

%o (PARI) {a(n)=sum(k=0,n,sum(m=1,n,(-1)^(m-1)* (matrix(n+1,n+1,i,j,if(i>j,binomial(i-1,j-1)^2))^m/m)[n+1,k+1]))}

%Y Cf. A008459, A002190, A101980, A101981.

%K sign

%O 0,3

%A _Paul D. Hanna_, Dec 23 2004