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A112701 Partial sum of Catalan numbers A000108 multiplied by powers of 7. 1
1, 8, 106, 1821, 35435, 741329, 16270997, 369570944, 8613236374, 204812473608, 4949266755812, 121188396669810, 3000342229924222, 74979188061284522, 1888846103011564082, 47915719069874907917, 1222954711282739097587 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..693

FORMULA

a(n) = Sum_{k=0..n} C(k)*7^k, n>=0, with C(n):=A000108(n).

G.f.: c(7*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.

Conjecture: (n+1)*a(n) +(-29*n+13)*a(n-1) +14*(2*n-1)*a(n-2)=0. - R. J. Mathar, Jun 08 2016

Conjecture verified using the d.e. (28*x^3-29*x^2+x)*y' + (42*x^2-16*x+1)*y=1 satisfied by the g.f. - Robert Israel, Aug 04 2020

MAPLE

f:= gfun:-rectoproc({(n+1)*a(n) +(-29*n+13)*a(n-1) +14*(2*n-1)*a(n-2)=0, a(0)=1, a(1)=8}, a(n), remember):

map(f, [$0..50]); # Robert Israel, Aug 04 2020

CROSSREFS

Eighth column (m=7) of triangle A112705.

Sequence in context: A055406 A155632 A129278 * A099695 A236953 A345474

Adjacent sequences:  A112698 A112699 A112700 * A112702 A112703 A112704

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 31 2005

STATUS

approved

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Last modified December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)