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A330436 a(n) = n * n!! - Sum_{k=1..n-1} k!! * a(n-k). 0
1, 3, 4, 19, 31, 168, 323, 1859, 4072, 24403, 59423, 368488, 980123, 6275139, 17998264, 118858755, 364059999, 2478263856, 8045642683, 56418223739, 192980878976, 1392909382923, 4995715059111, 37083230363840, 138896979832131, 1059335618366171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Logarithmic derivative of A006882.

LINKS

Table of n, a(n) for n=1..26.

FORMULA

L.g.f.: log(Sum_{k>=0} k!! * x^k).

MATHEMATICA

a[n_] := a[n] = n n!! - Sum[k!! a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 26}]

nmax = 26; CoefficientList[Series[Log[Sum[k!! x^k, {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest

CROSSREFS

Cf. A003319, A004208, A006882, A233824, A307064.

Sequence in context: A036253 A212113 A196133 * A025089 A041989 A196198

Adjacent sequences: A330433 A330434 A330435 * A330437 A330438 A330439

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 14 2019

STATUS

approved

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Last modified December 3 00:23 EST 2022. Contains 358510 sequences. (Running on oeis4.)