A173794 Partial sums of A006384.

1, 3, 7, 21, 78, 390, 2461, 17491, 135226, 1103076, 9371892, 82205622, 740254762, 6814312822, 63920746639, 609452784251, 5894288690288, 57728196873452, 571747727911362, 5719672404523644, 57737110684330278, 587604181217075742

Offset: 0

Author

Jonathan Vos Post, Feb 24 2010

Keywords

• nonn

Comments

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.

Examples

			a(21) = 1 + 2 + 4 + 14 + 57 + 312 + 2071 + 15030 + 117735 + 967850 + 8268816 + 72833730 + 658049140 + 6074058060 + 57106433817 + 545532037612 + 5284835906037 + 51833908183164 + 514019531037910 + 5147924676612282 + 52017438279806634 + 529867070532745464.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..900

Crossrefs

Cf. A000168, A006384.

Programs

Mathematica

q[n_?OddQ]:= 3^((n-1)/2)*CatalanNumber[(n-1)/2];
q[n_?EvenQ]:= 3^((n-2)/2)*(2*(n-1)/(n+2))*CatalanNumber[(n-2)/2];
f[n_]:= f[n]= Sum[EulerPhi[n/k]*3^k*Binomial[2*k, k], {k, Most[Divisors[n]]}];
A006384[n_]:= If[n==0, 1, (1/(2*n))*(2*(3^n/(n+2))*CatalanNumber[n] +f[n] + 2*n*q[n])];
Table[Sum[A006384[j], {j,0,n}], {n,0,50}] (* G. C. Greubel, Jul 14 2021 *)

Formula

a(n) = Sum_{i=0..n} A006384(i).