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A061160 Numerators in expansion of Euler transform of b(n) = 1/3. 4
1, 1, 5, 50, 215, 646, 8711, 25475, 105925, 3091270, 11691247, 36809705, 445872155, 1364113925, 5085042010, 50975292560, 183383680088, 588817265695, 19512559194875, 62369303509475, 224877933068647, 2214198452392027, 7686538660149565, 25124342108522750 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Denominators of c(n) are 3^d(n), where d(n)=power of 3 in (3*n)!, cf. A004128.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Geoffrey B. Campbell, Some n-space q-binomial theorem extensions and similar identities, arXiv:1906.07526 [math.NT], 2019.

Geoffrey B. Campbell, A. Zujev, Some almost partition theoretic identities, Preprint, 2016.

N. J. A. Sloane, Transforms

FORMULA

Numerators of c(n), where c(n) = (1/(3*n))*Sum_{k=1..n} c(n-k)*sigma(k), n>0, c(0)=1.

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, add(add(

      d/3, d=numtheory[divisors](j))*b(n-j), j=1..n)/n)

    end:

a:= n-> numer(b(n)):

seq(a(n), n=0..30);  # Alois P. Heinz, Jul 28 2017

CROSSREFS

Cf. A000712, A061159, A061161.

Sequence in context: A267640 A238650 A281606 * A226548 A274064 A302695

Adjacent sequences:  A061157 A061158 A061159 * A061161 A061162 A061163

KEYWORD

easy,nonn,frac

AUTHOR

Vladeta Jovovic, Apr 17 2001

STATUS

approved

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)