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 A002422 Expansion of (1-4*x)^(5/2). (Formerly M4692 N2003) 7
 1, -10, 30, -20, -10, -12, -20, -40, -90, -220, -572, -1560, -4420, -12920, -38760, -118864, -371450, -1179900, -3801900, -12406200, -40940460, -136468200, -459029400, -1556708400, -5318753700, -18296512728, -63334082520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 55. 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). T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 164. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 N. J. A. Sloane, Notes on A984 and A2420-A2424 FORMULA a(n) = sum[ m=0..n ] binomial(n, m) K_m(6), where K_m(x)=K_m(n, 2, x) is a Krawtchouk polynomial - abarg(AT)research.bell-labs.com (Alexander Barg). a(n) ~ -15/8*Pi^(-1/2)*n^(-7/2)*2^(2*n)*{1 + 35/8*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 22 2001 a(n) = -(15/8)*4^n*Gamma(n-5/2)/(sqrt(Pi)*Gamma(1+n)). - Peter Luschny, Dec 14 2015 a(n) = (-4)^n*binomial(5/2, n). - Peter Luschny, Oct 22 2018 MAPLE A002422 := n -> -(15/8)*4^n*GAMMA(n-5/2)/(sqrt(Pi)*GAMMA(1+n)): seq(A002422(n), n=0..26); # Peter Luschny, Dec 14 2015 MATHEMATICA CoefficientList[Series[(1-4x)^{5/2}, {x, 0, 30}], x] (* Vincenzo Librandi, Jun 11 2012 *) CROSSREFS Cf. A007054, A004001, A002420, A002421, A002423, A002424, A007272. a(n+3) = -2 * A007272(n). Sequence in context: A027979 A181102 A057456 * A031195 A034117 A104863 Adjacent sequences:  A002419 A002420 A002421 * A002423 A002424 A002425 KEYWORD sign AUTHOR STATUS approved

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Last modified November 21 04:21 EST 2018. Contains 317428 sequences. (Running on oeis4.)