|
| |
|
|
A062109
|
|
Expansion of (1-x)^4/(1-2x)^4.
|
|
10
| |
|
|
1, 4, 14, 44, 129, 360, 968, 2528, 6448, 16128, 39680, 96256, 230656, 546816, 1284096, 2990080, 6909952, 15859712, 36175872, 82051072, 185139200, 415760384, 929562624, 2069889024, 4591714304, 10150215680, 22364028928
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| If X_1,X_2,...,X_n are 2-blocks of a (2n+4)-set X then, for n>=1, a(n+1) is the number of (n+3)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 23 2007
If the offset here is set to zero, the binomial transform of A006918. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 29 2009]
a(n)= number of weak compositions of n with exeactly 3 parts are equal 0. [From Milan R. Janjic (agnus(AT)blic.net), Jun 27 2010]
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
Milan Janjic, Two Enumerative Functions
|
|
|
FORMULA
| a(n) =(n+5)*(n^2+13n+18)*2^(n-5)/3 [with a(0)=1] =A055809(n-5)*2^(n-4) =2a(n-1)+A058396(n)-A058396(n-1) =sum{k<n}[a(n)]+A058396(n) =A062110(4, n)
G.f.:(1-x)^4/(1-2x)^4.
|
|
|
PROG
| (PARI) a(n)=if(n<1, n==0, (n+5)*(n^2+13*n+18)*2^n/96)
(PARI) { a=1; for (n=0, 200, if (n, a=(n + 5)*(n^2 + 13*n + 18)*2^n/96); write("b062109.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 01 2009]
|
|
|
CROSSREFS
| Sequence in context: A099063 A057223 A007466 * A118042 A006645 A094309
Adjacent sequences: A062106 A062107 A062108 * A062110 A062111 A062112
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 30 2001
|
| |
|
|
