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A156733 Euler transform of n*A065958(n). 4
1, 1, 11, 41, 176, 606, 2391, 8091, 28636, 95056, 316048, 1014240, 3237325, 10082015, 31109500, 94352346, 283209381, 838650191, 2458835711, 7127912979, 20471486368, 58224189612, 164181018330, 458982667630, 1273039111210, 3503609456548, 9572771822745, 25971150308985 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to the g.f. of planar partitions (A000219): exp( Sum_{n>=1} sigma(n,2)*x^n/n ) = Product_{n>=1} 1/(1-x^n)^n.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000

FORMULA

a(n) = (1/n)*Sum_{k=1..n} sigma_2(k^2)*a(n-k) for n>0, with a(0) = 1.

G.f.: exp( Sum_{n>=1} A065827(n)*x^n/n ), where A065827(n) = sigma_2(n^2) is the sum of squares of the divisors of n^2. - Paul D. Hanna, Aug 09 2012

MAPLE

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

      a(n-j)*numtheory[sigma][2](j^2), j=1..n)/n)

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Sep 24 2016

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sigma(m^2, 2)*x^m/m)+x*O(x^n)), n)}

for(n=0, 21, print1(a(n), ", "))

CROSSREFS

Cf. A001157, A156303, A065827, A301978, A301980.

Sequence in context: A288795 A213659 A199209 * A079304 A260270 A118572

Adjacent sequences:  A156730 A156731 A156732 * A156734 A156735 A156736

KEYWORD

nonn

AUTHOR

Paul D. Hanna and Vladeta Jovovic, Feb 14 2009

STATUS

approved

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Last modified February 16 21:46 EST 2020. Contains 331975 sequences. (Running on oeis4.)