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A025232 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3. 4
3, 2, 12, 76, 504, 3472, 24672, 179792, 1337376, 10117312, 77618304, 602528640, 4724294400, 37361809920, 297683352576, 2387325283584, 19255919325696, 156110855965696, 1271401468151808 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

G.f.: (1-sqrt(1-12*x+28*x^2))/2 - Michael Somos, Jun 08 2000.

n*a(n)=(12*n-18)*a(n-1)-28*(n-3)*a(n-2) [Richard Choulet, Dec 16 2009]

a(n) ~ sqrt(3*sqrt(2)-2) * (2*(3+sqrt(2)))^n / (2*sqrt(14*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 11 2013

MATHEMATICA

Rest[CoefficientList[Series[(1-Sqrt[1-12*x+28*x^2])/2, {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 11 2013 *)

nxt[{n_, a_, b_, c_}]:={n+1, b, c, (c(12n-6)-28(n-2)*b)/(n+1)}; NestList[ nxt, {3, 3, 2, 12}, 20][[All, 2]] (* Harvey P. Dale, Jun 04 2019 *)

PROG

(PARI) a(n)=polcoeff((1-sqrt(1-12*x+28*x^2+x*O(x^n)))/2, n)

CROSSREFS

Sequence in context: A254215 A007214 A189736 * A236435 A218566 A125135

Adjacent sequences:  A025229 A025230 A025231 * A025233 A025234 A025235

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 16 15:51 EDT 2019. Contains 328101 sequences. (Running on oeis4.)