A117261 Row sums of triangle A117260.

1, 2, 5, 21, 169, 2705, 86561, 5539905, 709107841, 181531607297, 92944182936065, 95174843326530561, 194918079132734588929, 798384452127680876253185, 6540365431829961738266091521, 107157347235102093119751643480065, 3511331954199825387348021853554769921

Offset: 0

Author

Paul D. Hanna, Mar 14 2006

Keywords

• nonn

Crossrefs

Cf. A073587, A117260, A117263.

Programs

Mathematica

Table[Sum[2^((n(n-1))/2-(k(k-1))/2),{k,0,n}],{n,0,20}] (* Harvey P. Dale, Jul 05 2023 *)

PARI

a(n)=sum(k=0,n,2^((n-k)*(n+k-1)/2))

Formula

a(n) = Sum_{k=0..n} 2^(n*(n-1)/2 - k*(k-1)/2).

G.f. A(x) satisfies: A(x) = 1/(1 - x) + x * A(2*x). - Ilya Gutkovskiy, Jun 06 2020

a(n) = a(n-1) * 2^(n-1) + 1 for n > 0 and a(0) = 1. - Werner Schulte, Oct 17 2023