A061159 Numerators in expansion of Euler transform of b(n) = 1/2.
1, 1, 7, 17, 203, 455, 2723, 6001, 133107, 312011, 1613529, 3705303, 39159519, 88466147, 443939867, 1041952049, 40842931395, 93889422323, 460998957853, 1054706036923, 10194929714949, 23513104814105, 111438617932133, 255719229005751, 4864448363248503
Offset: 0
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, Continued Fractions for partition generating functions, arXiv:2301.12945 [math.CO], 2023.
- Geoffrey B. Campbell and A. Zujev, Some almost partition theoretic identities, Preprint, 2016.
- N. J. A. Sloane, Transforms
Programs
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Maple
b:= proc(n) option remember; `if`(n=0, 1, add(add( d/2, d=numtheory[divisors](j))*b(n-j), j=1..n)/n) end: a:= n-> numer(b(n)): seq(a(n), n=0..35); # Alois P. Heinz, Jul 28 2017
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Mathematica
c[n_] := c[n] = If[n == 0, 1, (1/(2n)) Sum[c[n-k] DivisorSigma[1, k], {k, 1, n}]]; a[n_] := Numerator[c[n]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Apr 24 2022 *)
Formula
Numerators of c(n), where c(n)=1/(2*n)*Sum_{k=1..n} c(n-k)*sigma(k), n>0, c(0)=1.
Comments