cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A112710 Partial sums of Catalan numbers A000108 multiplied by powers of -3.

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%I A112710 #3 Oct 12 2012 14:40:24
%S A112710 1,-2,16,-119,1015,-9191,87037,-851186,8531044,-87167702,904619302,
%T A112710 -9509144240,101036961052,-1083385595648,11708378016712,
%U A112710 -127402051267703,1394629704432367,-15347719608268403,169699299111055897,-1884322608673443833,21003350078068124587
%N A112710 Partial sums of Catalan numbers A000108 multiplied by powers of -3.
%C A112710 Fourth column (m=3) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).
%F A112710 a(n)= A112707(n+3, 3), n>=0.
%F A112710 G.f.: c(-3*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
%F A112710 G.f. for unsigned sequence: c(3*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*3^n} and {(-1)^n}, where C(n):=A000108(n).
%Y A112710 Cf. A064306 (unsigned m=2 case).
%K A112710 sign,easy
%O A112710 0,2
%A A112710 _Wolfdieter Lang_, Oct 31 2005