A001880 Coefficients of Bessel polynomials y_n (x). (Formerly M4989 N2146)

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

Offset

4,2

References

John 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, and 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], 2017-2019, Table 1.

J. Riordan, Notes to N. J. A. Sloane, Jul. 1968

Index entries for sequences related to Bessel functions or polynomials.

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

a(n) ~ 2^(n-5/2) * n^n / (3*exp(n)). - Amiram Eldar, Jul 11 2026

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 *)

Prog

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

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.

Sequence in context: A170696 A170734 A186231 * A240682 A113362 A252875

Adjacent sequences: A001877 A001878 A001879 * A001881 A001882 A001883

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved