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A117261
Row sums of triangle A117260.
3
1, 2, 5, 21, 169, 2705, 86561, 5539905, 709107841, 181531607297, 92944182936065, 95174843326530561, 194918079132734588929, 798384452127680876253185, 6540365431829961738266091521, 107157347235102093119751643480065, 3511331954199825387348021853554769921
OFFSET
0,2
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 14 2006
STATUS
approved

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Last modified September 20 02:41 EDT 2024. Contains 376016 sequences. (Running on oeis4.)