A117261 Row sums of triangle A117260.

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

Offset

0,2

Links

Table of n, a(n) for n=0..16.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A073587, A117260, A117263.

Sequence in context: A193189 A358316 A176527 * A108021 A162437 A357871

Adjacent sequences: A117258 A117259 A117260 * A117262 A117263 A117264

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved