

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
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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)/(1x), where c(x):=(1sqrt(14*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
Conjecture: (n+1)*a(n) +(29*n+13)*a(n1) +14*(2*n1)*a(n2)=0.  R. J. Mathar, Jun 08 2016
Conjecture verified using the d.e. (28*x^329*x^2+x)*y' + (42*x^216*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(n1) +14*(2*n1)*a(n2)=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



