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A163928 Numerators of the higher order exponential integral constants alpha(2,n). 2
0, 1, 21, 1897, 32197, 20881861, 7139587, 17462165587, 283355376967, 69621962857381, 70246946681461, 1036088178214798501, 1042504974775473001, 29931734181763981573561, 4295332813075795410223, 4312254507400142830831 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
See A163927 for information about the alpha(k,n) constants.
Apart from a difference of offset, alpha(2,n) appears to be the multiple harmonic (star) sum Sum_{j = 1..n} 1/j^2 Sum_{k = 1..j} 1/k^2, which has the initial values [1, 21/16, 1897/1296, 32197/20736, 20881861/12960000, 7139587/4320000, ...]. - Peter Bala, Jan 31 2019
LINKS
FORMULA
alpha(k,n) = (1/k)*Sum_{i=0..k-1} (Sum_{p=0..n-1} p^(-2*(k-i))*alpha(i, n) with alpha(0,n) = 1, with k = 2 and n >= 1. alpha(1,n) = A007406(n-1)/A007407(n-1) for n >= 2.
EXAMPLE
alpha(k=2,n=1) = 0, alpha(k=2,2) = 1, alpha(k=2,3) = 21/16, alpha(k=2,4) = 1897/1296.
MAPLE
nmax:=17; rowk:=2; kmax:=nmax: k:=0: for n from 1 to nmax do alpha(k, n):=1 od: for k from 1 to kmax do for n from 1 to nmax do alpha(k, n) := (1/k)*sum(sum(p^(-2*(k-i)), p=0..n-1)*alpha(i, n), i=0..k-1) od; od: seq(alpha(rowk, n), n=1..nmax);
CROSSREFS
Cf. A163929 (denominators).
Cf. A163927 (alpha(k,n)) and A090998 (gamma(k,n)).
Sequence in context: A232949 A305145 A296686 * A358803 A243685 A221122
KEYWORD
nonn,frac,easy
AUTHOR
Johannes W. Meijer & Nico Baken, Aug 13 2009, Aug 17 2009
STATUS
approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)