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A237670 Inverse Moebius transform of Catalan numbers. 1
1, 3, 6, 17, 43, 140, 430, 1447, 4868, 16841, 58787, 208166, 742901, 2674872, 9694893, 35359117, 129644791, 477643702, 1767263191, 6564137275, 24466267455, 91482622429, 343059613651, 1289904356920, 4861946401495, 18367353815055, 69533550920872 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..200

FORMULA

a(n) = Sum_{d|n} binomial(2*d,d)/(d+1).

G.f.: Sum_{k>=1} (1-2*x^k-sqrt(1-4*x^k))/(2*x^k).

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(binomial(2*k,k)/(k*(k+1)))) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 20 2018

MATHEMATICA

Table[Sum[Binomial[2 d, d]/(d + 1), {d, Divisors[n]}], {n, 1, 100}]

PROG

(Maxima) a(n) := lsum(binomial(2*d, d)/(d+1), d, listify(divisors(n)));

makelist(a(n), n, 1, 40);

(MAGMA) [&+[Binomial(2*d, d)/(d+1): d in Divisors(n)]: n in [1..40]]; // Bruno Berselli, Feb 11 2014

(PARI) a(n) = sumdiv(n, d, binomial(2*d, d)/(d+1)); \\ Michel Marcus, May 20 2018

CROSSREFS

Cf. A000108.

Sequence in context: A129905 A143363 A216878 * A321227 A006081 A099511

Adjacent sequences:  A237667 A237668 A237669 * A237671 A237672 A237673

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Feb 11 2014

STATUS

approved

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Last modified January 24 21:02 EST 2022. Contains 350565 sequences. (Running on oeis4.)