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A172320
11th column of A172119.
0
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2047, 4092, 8180, 16352, 32688, 65344, 130624, 261120, 521984, 1043456, 2085888, 4169729, 8335366, 16662552, 33308752, 66584816, 133104288, 266077952, 531894784, 1063267584
OFFSET
0,2
FORMULA
a(n)=sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))) with k=10.
G.f: f(z)=1/(1-2*z+z^(11)).
a(n+11)=2*a(n+10)-a(n).
EXAMPLE
a(12)=C(12,12)*2^12-C(2,1)*2^1=4092.
MAPLE
k:=10:taylor(1/(1-2*z+z^(k+1)), z=0, 30); for k from 0 to 20 do for n from 0 to 30 do b(n):=sum((-1)^j*binomial(n-k*j, n-(k+1)*j)*2^(n-(k+1)*j), j=0..floor(n/(k+1))):od:k: seq(b(n), n=0..30):od;
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Jan 31 2010
STATUS
approved