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A003472 a(n) = 2^(n-4)*C(n,4).
(Formerly M4718)
25
1, 10, 60, 280, 1120, 4032, 13440, 42240, 126720, 366080, 1025024, 2795520, 7454720, 19496960, 50135040, 127008768, 317521920, 784465920, 1917583360, 4642570240, 11142168576, 26528972800, 62704844800, 147220070400 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

Number of 4D hypercubes in n-dimensional hypercube. - Henry Bottomley, Apr 14 2000

With four leading zeros, binomial transform of C(n,4). - Paul Barry, Apr 10 2003

If X_1, X_2, ..., X_n is a partition of a 2n-set X into 2-blocks, then, for n>3, a(n) is equal to the number of (n+4)-subsets of X intersecting each X_i (i=1,2,...,n). - Milan Janjic, Jul 21 2007

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 796.

Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009, page 282.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 4..400

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

H. J. Brothers, Pascal's Prism: Supplementary Material.

H. Izbicki, Über Unterbaeume eines Baumes, Monatshefte für Mathematik, 74 (1970), 56-62.

H. Izbicki, Über Unterbaeume eines Baumes, Monatshefte für Mathematik, 74 (1970), 56-62.

Milan Janjic, Two Enumerative Functions

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013

C. W. Jones, J. C. P. Miller, J. F. C. Conn, R. C. Pankhurst, Tables of Chebyshev polynomials Proc. Roy. Soc. Edinburgh. Sect. A. 62, (1946). 187-203.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

John Riordan and N. J. A. Sloane, Correspondence, 1974

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32)

FORMULA

a(n) = 2*a(n-1) + A001789(n-1).

G.f.: 1/(1-2*x)^5;  e.g.f.: exp(2*x)(x^4/4!) (with 4 leading zeros). - Paul Barry, Apr 10 2003

MAPLE

A003472:=-1/(2*z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation

seq(binomial(n, 4)*2^(n-4), n=4..24); # Zerinvary Lajos, Jun 12 2008

MATHEMATICA

Table[2^(n-4) Binomial[n, 4], {n, 4, 50}] (* or *) LinearRecurrence[{10, -40, 80, -80, 32}, {1, 10, 60, 280, 1120}, 50] (* Harvey P. Dale, May 27 2017 *)

PROG

(MAGMA) [2^(n-4)* Binomial(n, 4): n in [4..30]]; // Vincenzo Librandi, Oct 16 2011

(PARI) a(n)=binomial(n, 4)<<(n-4) \\ Charles R Greathouse IV, May 18 2015

CROSSREFS

Cf. A001787, A001788, A001789.

Sequence in context: A241929 A278721 A004406 * A112502 A083585 A250575

Adjacent sequences:  A003469 A003470 A003471 * A003473 A003474 A003475

KEYWORD

nonn,easy,nice,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Apr 15 2000

STATUS

approved

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Last modified June 25 22:15 EDT 2017. Contains 288730 sequences.