A065949 Bessel polynomial {y_n}'''(0).

0, 0, 0, 90, 630, 2520, 7560, 18900, 41580, 83160, 154440, 270270, 450450, 720720, 1113840, 1670760, 2441880, 3488400, 4883760, 6715170, 9085230, 12113640, 15939000, 20720700, 26640900, 33906600, 42751800, 53439750, 66265290, 81557280, 99681120, 121041360, 146084400

Offset: 0

Author

N. J. A. Sloane, Dec 08 2001

Keywords

• nonn
• easy

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to Bessel functions or polynomials
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A001518, A001516.

Programs

Mathematica

Drop[90*Binomial[Range[40]-3,6],5] (* Harvey P. Dale, Sep 20 2013 *)

PARI

for(n=0,50, print1(90*binomial(n+3,6), ", ")) \\ G. C. Greubel, Aug 15 2017

Formula

a(n) = 90 * C(n-3, 6) = 90 * A000579(n-3). - Ralf Stephan, Sep 03 2003

From Colin Barker, Aug 01 2013: (Start)

a(n) = ((-2+n)*(-1+n)*n*(1+n)*(2+n)*(3+n))/8.

G.f.: -90*x^3 / (x-1)^7. (End)

E.g.f.: (1/8)*x^3*(120 + 90*x + 18*x^2 + x^3)*exp(x). - G. C. Greubel, Aug 15 2017

Extensions

More terms from Colin Barker, Aug 01 2013