

A259409


The pibased arithmetic derivative of the double factorial of n.


2



0, 0, 1, 2, 12, 19, 128, 193, 1600, 2997, 20224, 37692, 319488, 552366, 5164032, 10853055, 103268352, 198691110, 2199453696, 4050806490, 49934499840, 102089892240, 1176592711680, 2471811316695, 32489204613120, 71282307214125, 893769083781120, 2351538388135125
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OFFSET

0,4


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..800


FORMULA

a(n) = A258851(n!!) = A258851(A006882(n)).


MAPLE

with(numtheory):
d:= n> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
a:= proc(n) option remember;
`if`(n<2, 0, a(n2)*n+doublefactorial(n2)*d(n))
end:
seq(a(n), n=0..40);


CROSSREFS

Cf. A006882, A258845, A258851.
Sequence in context: A048001 A109299 A216629 * A073257 A240905 A303880
Adjacent sequences: A259406 A259407 A259408 * A259410 A259411 A259412


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Jun 26 2015


STATUS

approved



