cp's OEIS Frontend

A173794 Partial sums of A006384.

%I A173794 #5 Jul 14 2021 20:29:52
%S A173794 1,3,7,21,78,390,2461,17491,135226,1103076,9371892,82205622,740254762,
%T A173794 6814312822,63920746639,609452784251,5894288690288,57728196873452,
%U A173794 571747727911362,5719672404523644,57737110684330278,587604181217075742
%N A173794 Partial sums of A006384.
%C A173794 Partial sums of number of planar maps with n edges. The subsequence of primes in this partial sum begins: 3, 7, 17491, and no more known.
%H A173794 G. C. Greubel, <a href="/A173794/b173794.txt">Table of n, a(n) for n = 0..900</a>
%F A173794 a(n) = Sum_{i=0..n} A006384(i).
%e A173794 a(21) = 1 + 2 + 4 + 14 + 57 + 312 + 2071 + 15030 + 117735 + 967850 + 8268816 + 72833730 + 658049140 + 6074058060 + 57106433817 + 545532037612 + 5284835906037 + 51833908183164 + 514019531037910 + 5147924676612282 + 52017438279806634 + 529867070532745464.
%t A173794 q[n_?OddQ]:= 3^((n-1)/2)*CatalanNumber[(n-1)/2];
%t A173794 q[n_?EvenQ]:= 3^((n-2)/2)*(2*(n-1)/(n+2))*CatalanNumber[(n-2)/2];
%t A173794 f[n_]:= f[n]= Sum[EulerPhi[n/k]*3^k*Binomial[2*k, k], {k, Most[Divisors[n]]}];
%t A173794 A006384[n_]:= If[n==0, 1, (1/(2*n))*(2*(3^n/(n+2))*CatalanNumber[n] +f[n] + 2*n*q[n])];
%t A173794 Table[Sum[A006384[j], {j,0,n}], {n,0,50}] (* _G. C. Greubel_, Jul 14 2021 *)
%Y A173794 Cf. A000168, A006384.
%K A173794 nonn
%O A173794 0,2
%A A173794 _Jonathan Vos Post_, Feb 24 2010