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A003472
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2^(n-4)*C(n,4).
(Formerly M4718)
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20
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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; internal format)
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OFFSET
| 4,2
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COMMENTS
| Number of 4D hypercubes in n-dimensional hypercube - Henry Bottomley (se16(AT)btinternet.com), Apr 14 2000.
With four leading zeros, binomial transform of C(n,4) - Paul Barry (pbarry(AT)wit.ie), 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 R. Janjic (agnus(AT)blic.net), Jul 21 2007
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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.
H. J. Brothers, Pascal's Prism: Supplementary Material, http://www.brotherstechnology.com/docs/Pascal's_Prism_(supplement).pdf.
H. Izbicki, Ueber Unterbaeume eines Baumes, Monatshefte f\"{u}r Mathematik, 74 (1970), 56-62.
Jones, C. W.; Miller, J. C. P.; Conn, J. F. C.; Pankhurst, R. C.; Tables of Chebyshev polynomials. Proc. Roy. Soc. Edinburgh. Sect. A. 62, (1946). 187-203.
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).
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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].
Milan Janjic, Two Enumerative Functions
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to Chebyshev polynomials.
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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 (pbarry(AT)wit.ie), Apr 10 2003
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MAPLE
| A003472:=-1/(2*z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
seq(binomial(n, 4)*2^(n-4), n=4..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008
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PROG
| (MAGMA) [2^(n-4)* Binomial(n, 4): n in [4..30]]; // Vincenzo Librandi, Oct 16 2011
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CROSSREFS
| Cf. A001787, A001788, A001789.
Sequence in context: A144560 A076160 A004406 * A112502 A083585 A155633
Adjacent sequences: A003469 A003470 A003471 * A003473 A003474 A003475
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 15 2000
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