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A157019 Sum_{d|n} binomial(n/d+d-2,d-1). 6
1, 2, 2, 4, 2, 8, 2, 10, 8, 12, 2, 34, 2, 16, 32, 38, 2, 62, 2, 92, 58, 24, 2, 210, 72, 28, 92, 198, 2, 394, 2, 274, 134, 36, 422, 776, 2, 40, 184, 1142, 2, 1178, 2, 618, 1232, 48, 2, 2634, 926, 1482, 308, 964, 2, 2972, 2004, 4610, 382, 60, 2, 8576, 2, 64, 6470, 5130 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals row sums of triangle A156348. - Gary W. Adamson & Mats Granvik, Feb 21 2009

a(n) = 2 iff n is prime.

The binomial transform (note the offset) is 0, 1, 4, 11, 28, 67, 156, 359, 818, 1847, 4146, 9275,... - R. J. Mathar, Mar 03 2013

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: A(x) = Sum_{n>=1} x^n/(1 - x^n)^n. [From Paul D. Hanna, Mar 01 2009]

EXAMPLE

a(4) = 4 = (1 + 2 + 0 + 1).

MAPLE

A157019 := proc(n) add( binomial(n/d+d-2, d-1), d=numtheory[divisors](n) ) ; end:

PROG

(PARI) {a(n)=polcoeff(sum(m=1, n, x^m/(1-x^m+x*O(x^n))^m), n)} [From Paul D. Hanna, Mar 01 2009]

CROSSREFS

Cf. A081543, A018818, A156838 (Mobius transform).

Cf. A156348.

Sequence in context: A190014 A100577 A018818 * A067538 A096154 A270365

Adjacent sequences:  A157016 A157017 A157018 * A157020 A157021 A157022

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Feb 21 2009

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.