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A057788
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Expansion of (1+x)/(1-x)^12.
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5
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1, 13, 90, 442, 1729, 5733, 16744, 44200, 107406, 243542, 520676, 1058148, 2057510, 3848222, 6953544, 12183560, 20764055, 34512075, 56071470, 89224590, 139299615, 213696795, 322561200, 479634480, 703323660, 1018031196, 1455797448
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 1/2^10 of twelfth unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted).
If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-12) is the number of 12-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
11-dimensional square numbers, tenth partial sums of binomial transform of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+10,i+10)*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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LINKS
| Milan Janjic, Two Enumerative Functions
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)=2*C(n+11, 11)-C(n+10, 10). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003
a(n)=C(n+10,10)+2*C(n+10,11) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]
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MAPLE
| A057788 := proc(n)
1/39916800*(2*n+11) *(n+10) *(n+9) *(n+8) *(n+7) *(n+6) *(n+5) *(n+4) *(n+3) *(n+2) *(n+ 1) ; end proc: # R. J. Mathar, Mar 22 2011
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MATHEMATICA
| s1=s2=s3=s4=s5=s6=s7=s8=s9=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; s8+=s7; s9+=s8; AppendTo[lst, s9], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
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CROSSREFS
| Cf. A054334, A054333, A053347, A002415.
Cf. A005585, A040977, A050486 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
Partial sums of A054334 [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]
Sequence in context: A161465 A162300 A161859 * A166215 A131700 A156947
Adjacent sequences: A057785 A057786 A057787 * A057789 A057790 A057791
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 04 2000
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