A001881 Coefficients of Bessel polynomials y_n (x). (Formerly M5116 N2217)

1, 21, 378, 6930, 135135, 2837835, 64324260, 1571349780, 41247931725, 1159525191825, 34785755754750, 1109981842719750, 37554385678684875, 1343291487737574375, 50661278966102805000, 2009564065655411265000, 83648104232906493905625, 3646073249210806587298125

Offset

5,2

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

G. C. Greubel, Table of n, a(n) for n = 5..400 (terms 5..100 from T. D. Noe)

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

Formula

a(n) = (2n-5)!/( 5!*(n-5)!*2^(n-5) ).

a(n) = binomial(n-3,2)*(2*n-5)!!/5!!, n >= 5, with (2*n-5)!! = A001147(n-2).

E.g.f.: x*(1 + 3*x/2)/(1 - 2*x)^(9/2), with offset 1. - G. C. Greubel, Aug 13 2017

G.f.: t^5 * hypergeometric2F0(3, 7/2; -; 2*t) = t^5 + 21*t^6 + .... - G. C. Greubel, Aug 16 2017

Mathematica

With[{nn = 50}, CoefficientList[Series[x*(1 + 3*x/2)/(1 - 2*x)^(9/2), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 13 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(serlaplace(x*(1 + 3*x/2)/(1 - 2*x)^(9/2))) \\ G. C. Greubel, Aug 13 2017
(Magma) [Factorial(2*n-5)/(120*Factorial(n-5)*2^(n-5) ): n in [5..30]]; // Vincenzo Librandi, Aug 14 2017

Crossrefs

See A001518.

(1/4) the coefficient of x^2 of polynomials in A098503.

Column 5 of triangle A001497.

Third column (m=2) of Laguerre-Sonin a=1/2 triangle A130757.

Sequence in context: A181364 A134494 A004370 * A240683 A108740 A297455

Adjacent sequences: A001878 A001879 A001880 * A001882 A001883 A001884

Keyword

nonn,easy

Author

N. J. A. Sloane, Simon Plouffe

Status

approved