A110125 Row sums of a scaled Legendre triangle.

1, 1, 1, 9, 43, 213, 1507, 12537, 114325, 1144221, 12512373, 148351881, 1892798733, 25816700309, 374406371121, 5748436717505, 93098093268755, 1585364420710205, 28305454044441843, 528500175862180033, 10295596472841577779

Offset: 0

Author

Paul Barry, Jul 13 2005

Keywords

• easy
• nonn

Comments

Row sums of A110124.

Links

• Robert Israel, Table of n, a(n) for n = 0..478

Programs

Maple

f := n -> add(2^(n-k)*orthopoly[P](n-k,k),k=0..n):
map(f, [$0..30]); # Robert Israel, Jun 17 2019

PARI

a(n)=sum(k=0,n, pollegendre(n-k, k)<<(n-k)) \\ Charles R Greathouse IV, Mar 19 2017

Formula

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