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A054334
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1/512 of eleventh unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted).
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8
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1, 12, 77, 352, 1287, 4004, 11011, 27456, 63206, 136136, 277134, 537472, 999362, 1790712, 3105322, 5230016, 8580495, 13748020, 21559395, 33153120, 50075025, 74397180, 108864405, 157073280, 223689180, 314707536, 437766252, 602516992
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Partial sums of A054333.
If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-11) is the number of 11-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
10-dimensional square numbers, ninth partial sums of binomial transform of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+9,i+9)*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
| 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.
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LINKS
| 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.
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FORMULA
| a(n) = (2*n+10)*binomial(n+9, 9)/10 = ((-1)^n)*A053120(2*n+10, 10)/2^9.
G.f. (1+x)/(1-x)^11.
a(n)=2*C(n+10, 10)-C(n+9, 9). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003
a(n)=C(n+9,9)+2*C(n+9,10) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]
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MATHEMATICA
| s1=s2=s3=s4=s5=s6=s7=s8=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; s8+=s7; AppendTo[lst, s8], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
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CROSSREFS
| Cf. A053120, A054333.
Cf. A005585, A040977, A050486, A053347, A054333 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
Sequence in context: A161461 A162297 A161858 * A026964 A026974 A109711
Adjacent sequences: A054331 A054332 A054333 * A054335 A054336 A054337
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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