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

0,2

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.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000168, A006384.

Sequence in context: A075211 A075212 A319123 * A049365 A288849 A031885

Adjacent sequences: A173791 A173792 A173793 * A173795 A173796 A173797

Keyword

nonn

Author

Jonathan Vos Post, Feb 24 2010

Status

approved