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A308939 Expansion of e.g.f. 1 / (1 - Sum_{k>=1} (2*k - 1)!!*x^k/k!). 0
1, 1, 5, 39, 411, 5445, 86805, 1616895, 34448715, 826093485, 22017673125, 645633501975, 20655688959675, 715958472554325, 26726481024167925, 1068988088284491375, 45608095005687088875, 2067503007329827192125, 99238033465208117605125, 5027986481205385725402375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

E.g.f.: 1/(2 - 1/sqrt(1 - 2*x)).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (2*k - 1)!! * a(n-k).

a(n) ~ n! * 8^n / 3^(n+1). - Vaclav Kotesovec, Jul 01 2019

D-finite with recurrence: +3*a(n) +(-14*n+9)*a(n-1) +8*(n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jan 27 2020

MATHEMATICA

nmax = 19; CoefficientList[Series[1/(2 - 1/Sqrt[1 - 2 x]), {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (2 k - 1)!! a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]

CROSSREFS

Cf. A001147, A002866, A295553.

Sequence in context: A316654 A070767 A124549 * A317618 A024216 A127189

Adjacent sequences:  A308936 A308937 A308938 * A308940 A308941 A308942

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 01 2019

STATUS

approved

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Last modified March 30 05:41 EDT 2020. Contains 333118 sequences. (Running on oeis4.)