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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..1000

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

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

N. J. A. Sloane

STATUS

approved

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Last modified February 18 03:43 EST 2018. Contains 299298 sequences. (Running on oeis4.)