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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
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
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
MATHEMATICA
a[0] = 1;
a[n_] := a[n] = (1/n) Sum[DivisorSigma[2, k^2] a[n-k], {k, 1, n}];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 03 2020 *)
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
KEYWORD
nonn
AUTHOR
STATUS
approved