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A054333 1/256 of tenth unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted). 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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]

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. 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.

LINKS

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).

FORMULA

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]

MATHEMATICA

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]

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Wolfdieter Lang, Mar 15 2000.

STATUS

approved

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Last modified April 17 18:00 EDT 2014. Contains 240655 sequences.