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A054333
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1/256 of tenth unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted).
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10
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1, 11, 65, 275, 935, 2717, 7007, 16445, 35750, 72930, 140998, 260338, 461890, 791350, 1314610, 2124694, 3350479, 5167525, 7811375, 11593725, 16921905, 24322155, 34467225, 48208875, 66615900, 91018356, 123058716, 164750740
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OFFSET
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0,2
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COMMENTS
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If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-10) is the number of 10-subsets of X intersecting both Y and Z. - Milan Janjic, Sep 08 2007
9-dimensional square numbers, eighth partial sums of binomial transform of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+8,i+8)*b(i)}, where b(i)=[1,2,0,0,0,...]. [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795.
Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
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LINKS
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Table of n, a(n) for n=0..27.
Milan Janjic, Two Enumerative Functions
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].
Index entries for sequences related to Chebyshev polynomials.
Index to sequences with linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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a(n) = (2*n+9)*binomial(n+8, 8)/9 = ((-1)^n)*A053120(2*n+9, 9)/2^8. G.f. (1+x)/(1-x)^10.
a(n)=2*C(n+9, 9)-C(n+8, 8). - Paul Barry, Mar 04 2003
a(n)=C(n+8,8)+2*C(n+8,9) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]
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MATHEMATICA
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s1=s2=s3=s4=s5=s6=s7=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; AppendTo[lst, s7], {n, 0, 7!}]; lst [From Vladimir Joseph Stephan Orlovsky, Jan 15 2009]
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CROSSREFS
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Partial sums of A053347. Cf. A053120, A000581.
Cf. A005585, A040977, A050486, A053347 [From Vladimir Joseph Stephan Orlovsky, Jan 15 2009]
Cf. A111125, fifth column (s=4, without leading zeros). [From Wolfdieter Lang, Oct 18 2012]
Sequence in context: A161459 A162288 A161776 * A036601 A125321 A054490
Adjacent sequences: A054330 A054331 A054332 * A054334 A054335 A054336
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KEYWORD
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nonn,easy
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AUTHOR
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Barry E. Williams, Wolfdieter Lang, Mar 15 2000.
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STATUS
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approved
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