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A061161 Numerators in expansion of Euler transform of b(n) = 1/4.

%I A061161 #23 Apr 24 2022 06:31:07
%S A061161 1,1,13,55,1235,4615,55801,200343,8977475,36804235,367235363,
%T A061161 1444888289,32062742231,120729974115,1205864254225,5201022002071,
%U A061161 395884671433315,1603069490974835,15989295873680415,64312573140322525,1250332447587844829,5262481040435242585
%N A061161 Numerators in expansion of Euler transform of b(n) = 1/4.
%C A061161 Denominators of c(n) are 2^A004134(n).
%H A061161 Alois P. Heinz, <a href="/A061161/b061161.txt">Table of n, a(n) for n = 0..1000</a>
%H A061161 Geoffrey B. Campbell and A. Zujev, <a href="http://zujev.physics.ucdavis.edu/papers/Some%20almost%20partition%20theoretic%20identities.pdf">Some almost partition theoretic identities</a>, Preprint, 2016.
%H A061161 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A061161 Numerators of c(n), where c(n) = (1/(4*n))*Sum_{k=1..n} c(n-k)*sigma(k), n>0, c(0)=1.
%p A061161 b:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A061161       d/4, d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
%p A061161     end:
%p A061161 a:= n-> numer(b(n)):
%p A061161 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jul 28 2017
%t A061161 c[n_] := c[n] = If[n == 0, 1,
%t A061161      (1/(4n)) Sum[c[n-k] DivisorSigma[1, k], {k, 1, n}]];
%t A061161 a[n_] := Numerator[c[n]];
%t A061161 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 24 2022 *)
%Y A061161 Cf. A000712, A061159, A061160.
%K A061161 easy,nonn,frac
%O A061161 0,3
%A A061161 _Vladeta Jovovic_, Apr 17 2001