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%I #9 Nov 05 2016 07:21:18
%S 0,3,13,38,94,213,459,960,1972,4007,8089,16266,32634,65385,130903,
%T 261956,524080,1048347,2096901,4194030,8388310,16776893,33554083,
%U 67108488,134217324,268435023,536870449,1073741330,2147483122,4294966737,8589933999,17179868556,34359737704,68719476035,137438952733,274877906166,549755813070,1099511626917,2199023254651,4398046510160
%N Column 1 of triangle A277410.
%F Conjectures from _Colin Barker_, Nov 04 2016: (Start)
%F G.f.: x^2*(3-2*x) / ((1-x)^3*(1-2*x)).
%F a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4) for n>4.
%F a(n) = (8*(2^n-1)-n*(n+7))/2. (End)
%o (PARI) {A277410(n, k) = my(A=x); for(i=1, n, A = x + subst(intformal(A +x*O(x^n)), x, y*A + (1-y)*x ) ); n!*polcoeff(polcoeff(A, n, x), k, y)}
%o for(n=1, 30, print1(A277410(n+1, 1), ", "));
%Y Cf. A277410, A277412.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Oct 25 2016
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