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A014333 Three-fold exponential convolution of Catalan numbers with themselves. 1
1, 3, 12, 57, 306, 1806, 11508, 78147, 559962, 4201038, 32792472, 264946446, 2206077804, 18860908644, 165050642736, 1474389557739, 13413397423482, 124030117316238, 1163661348170328, 11060842687616610, 106377560784576612, 1034009073326130876 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

FORMULA

E.g.f.: exp(6*x)*(BesselI(0,2*x) - BesselI(1,2*x))^3. - Ilya Gutkovskiy, Nov 01 2017

From Vaclav Kotesovec, Nov 13 2017: (Start)

Recurrence: (n+1)*(n+2)*(n+3)*a(n) = 4*(6*n^3 + 13*n^2 + 2*n - 3)*a(n-1) - 4*(n-1)*(44*n^2 - 16*n - 21)*a(n-2) + 192*(n-2)*(n-1)*(2*n - 3)*a(n-3).

a(n) ~ 2^(2*n) * 3^(n + 9/2) / (Pi^(3/2) * n^(9/2)). (End)

MATHEMATICA

nmax = 20; CoefficientList[Series[E^(6*x)*(BesselI[0, 2*x] - BesselI[1, 2*x])^3, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Nov 13 2017 *)

CROSSREFS

Cf. A000108, A014330.

Sequence in context: A159609 A128326 A323631 * A185618 A027710 A307495

Adjacent sequences:  A014330 A014331 A014332 * A014334 A014335 A014336

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)