A110125 - OEIS

%I #11 Jun 17 2019 15:21:15

%S 1,1,1,9,43,213,1507,12537,114325,1144221,12512373,148351881,

%T 1892798733,25816700309,374406371121,5748436717505,93098093268755,

%U 1585364420710205,28305454044441843,528500175862180033,10295596472841577779

%N Row sums of a scaled Legendre triangle.

%C Row sums of A110124.

%H Robert Israel, <a href="/A110125/b110125.txt">Table of n, a(n) for n = 0..478</a>

%F a(n)=sum{k=0..n, 2^(n-k)*LegendreP(n-k, k)}.

%p f := n -> add(2^(n-k)*orthopoly[P](n-k,k),k=0..n):

%p map(f, [$0..30]); # _Robert Israel_, Jun 17 2019

%o (PARI) a(n)=sum(k=0,n, pollegendre(n-k, k)<<(n-k)) \\ _Charles R Greathouse IV_, Mar 19 2017

%K easy,nonn

%O 0,4

%A _Paul Barry_, Jul 13 2005