A065947 Bessel polynomial {y_n}''(3).

0, 0, 6, 300, 13320, 620130, 31406550, 1743174216, 105889417200, 7010411889690, 503353562247360, 39003404559533700, 3246506259033473436, 289042023964190515200, 27418894569798460848210, 2761554229456140638184840, 294364593823858690215256200

Offset

0,3

References

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.

Links

G. C. Greubel, Table of n, a(n) for n = 0..340

Index entries for sequences related to Bessel functions or polynomials

Formula

From G. C. Greubel, Aug 14 2017: (Start)

a(n) = 4*n*(n - 1)*(1/2)_{n}*6^(n - 2)*hypergeometric1F1[(2-n, -2*n, 2/3), where (a)_{n} is the Pochhammer symbol.

E.g.f.: (-1/81)*(1 - 6*x)^(-5/2)*((171*x^2 - 90*x + 8)*sqrt(1 - 6*x) + (54*x^3 - 648*x^2 + 114*x - 8))*exp((1 - sqrt(1 - 6*x))/3). (End)

G.f.: (6*x^2/(1-x)^5)*hypergeometric2F0(3,5/2; - ; 6*x/(1-x)^2). - G. C. Greubel, Aug 16 2017

Mathematica

Join[{0, 0}, Table[4*n*(n - 1)*Pochhammer[1/2, n]*6^(n - 2)* Hypergeometric1F1[2 - n, -2*n, 2/3], {n, 2, 50}]] (* G. C. Greubel, Aug 14 2017 *)

Prog

(PARI) for(n=0, 50, print1(sum(k=0, n-2, ((n+k+2)!/(4*k!*(n-k-2)!))*(3/2)^k), ", ")) \\ G. C. Greubel, Aug 14 2017

Crossrefs

Cf. A001516, A001518.

Sequence in context: A197165 A264706 A066718 * A277168 A081321 A159494

Adjacent sequences: A065944 A065945 A065946 * A065948 A065949 A065950

Keyword

nonn

Author

N. J. A. Sloane, Dec 08 2001

Status

approved