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URL: https://oeis.org/A001881

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A001881
Coefficients of Bessel polynomials y_n (x).
8
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).
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
KEYWORD
nonn,easy
STATUS
approved