A001880 Coefficients of Bessel polynomials y_n (x).

1, 15, 210, 3150, 51975, 945945, 18918900, 413513100, 9820936125, 252070693875, 6957151150950, 205552193096250, 6474894082531875, 216659917377028125, 7675951358500425000, 287080580807915895000, 11303797869311688365625, 467445288360359818884375

Offset: 4

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 4..100
• Selden Crary, Richard Diehl Martinez, Michael Saunders, The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters, arXiv:1707.00705 [stat.ME], 2017, Table 1.
• J. Riordan, Notes to N. J. A. Sloane, Jul. 1968
• Index entries for sequences related to Bessel functions or polynomials

Crossrefs

See A001518.

Column 4 of triangle A001497.

Equals the second right hand column of the triangles A094665 and A083061.

Other right hand columns are A001147, A160470, A160471 and A160472.

Programs

Mathematica

nn = 25; t = Range[0, nn]! CoefficientList[Series[x (1 + x/2)/(1 - 2 x)^(7/2), {x, 0, nn}], x]; Drop[t, 1] (* T. D. Noe, Aug 10 2012 *)

PARI

x='x+O('x^50); Vec(serlaplace(x*(1 + x/2)/(1 - 2*x)^(7/2))) \\ G. C. Greubel, Aug 13 2017

Formula

E.g.f.: x*(1 + x/2)/(1 - 2*x)^(7/2); or, if shifted, (1+ 6x+ 3x^2/2!) / (1-2x)^(9/2).

a(n) = (2*n-4)!/(4!*(n-4)!*2^(n-4)).

(n-4)*a(n) = (n-2)*(2*n-5)*a(n-1) for n = 5, 6, .. , with a(4) = 1. - Johannes W. Meijer, May 24 2009

G.f.: x^4*2F0(5/2,3;;2x). - R. J. Mathar, Aug 08 2015