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A173794 Partial sums of A006384. 1
1, 3, 7, 21, 78, 390, 2461, 17491, 135226, 1103076, 9371892, 82205622, 740254762, 6814312822, 63920746639, 609452784251, 5894288690288, 57728196873452, 571747727911362, 5719672404523644, 57737110684330278, 587604181217075742 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 12 00:34 EDT 2022. Contains 356067 sequences. (Running on oeis4.)