|
|
A061159
|
|
Numerators in expansion of Euler transform of b(n) = 1/2.
|
|
5
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Denominators of c(n) are 2^d(n), where d(n)=power of 2 in (2n)!, cf. A005187.
|
|
LINKS
|
|
|
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.
|
|
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)):
|
|
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]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|