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A259409 The pi-based 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 (list; graph; refs; listen; history; text; internal format)
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(n-2)*n+doublefactorial(n-2)*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

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Last modified December 7 17:41 EST 2019. Contains 329847 sequences. (Running on oeis4.)