|
| |
|
|
A053347
|
|
C(n+7, 7)*(n+4)/4.
|
|
13
| |
|
|
1, 10, 54, 210, 660, 1782, 4290, 9438, 19305, 37180, 68068, 119340, 201552, 329460, 523260, 810084, 1225785, 1817046, 2643850, 3782350, 5328180, 7400250, 10145070, 13741650, 18407025, 24402456, 32040360, 41692024, 53796160
(list; graph; refs; listen; history; 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-9) is the number of 9-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
8-dimensional square numbers, seventh partial sums of binomial transform of [1, 2, 0, 0, 0, ...]. a(n) = sum{i=0,n,C(n+7, i+7)*b(i)}, where b(i) = [1, 2, 0, 0, 0, ...]. - Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009
|
|
|
REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
|
|
|
LINKS
| Milan Janjic, Two Enumerative Functions
Index entries for sequences related to linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Index entries for sequences related to Chebyshev polynomials.
|
|
|
FORMULA
| a(n) = ((-1)^n)*A053120(2*n+8, 8)/2^7 (1/128 of ninth unsigned column of Chebyshev T-triangle, zeros omitted).
G.f.: (1+x)/(1-x)^9.
a(n) = 2*C(n+8, 8)-C(n+7, 7). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003
Equals A027803/35 = C(n+4, n)*C(n+7, 4)/35 - Zerinvary Lajos (zlaja(AT)freemail.hu), May 25 2005
a(n) = C(n+7, 7)+2*C(n+7, 8) - Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009
|
|
|
MATHEMATICA
| s1=s2=s3=s4=s5=s6=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; AppendTo[lst, s6], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
|
|
|
PROG
| (PARI) a(n)=binomial(n+7, 7)*(n+4)/4 \\ Charles R Greathouse IV, Jun 10 2011
|
|
|
CROSSREFS
| Partial sums of A050486.
Cf. A005585, A040977, A050486.
Sequence in context: A161458 A162248 A161755 * A036600 A058645 A170940
Adjacent sequences: A053344 A053345 A053346 * A053348 A053349 A053350
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Barry E. Williams, Jan 06 2000
|
| |
|
|
