login
Expansion of 1/(1-6x*c(7x)), where c(x) is the g.f. of A000108.
2

%I #13 May 11 2019 02:21:08

%S 1,6,78,1308,24942,513876,11148012,250917624,5805563310,137233668900,

%T 3299955883428,80468668049160,1985171406618156,49458290358431688,

%U 1242613072013591832,31448339835422435568

%N Expansion of 1/(1-6x*c(7x)), where c(x) is the g.f. of A000108.

%F G.f.: 7/(4 + 3*sqrt(1-28*x)).

%F a(n) = 7^n*Sum_{j=0..n} (6/7)^j*j*binomial(2n-j,n)/(2n-j) for n >= 1. - _Emeric Deutsch_, Nov 19 2007

%F a(n) = Sum_{k=0..n} A039599(n,k)*(-1)^k*7^(n-k). - _Philippe Deléham_, Dec 11 2007

%p g:=7/(4+3*sqrt(1-28*x)): gser:=series(g,x=0,18): seq(coeff(gser,x,n),n=0..15); # _Emeric Deutsch_, Nov 19 2007

%K nonn

%O 0,2

%A _Philippe Deléham_, Nov 18 2007

%E More terms from _Emeric Deutsch_, Nov 19 2007