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A058396
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Expansion of (1-x)^3/(1-2x)^3.
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19
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1, 3, 9, 25, 66, 168, 416, 1008, 2400, 5632, 13056, 29952, 68096, 153600, 344064, 765952, 1695744, 3735552, 8192000, 17891328, 38928384, 84410368, 182452224, 393216000, 845152256, 1811939328, 3875536896, 8271167488, 17616076800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| If X_1,X_2,...,X_n are 2-blocks of a (2n+3)-set X then, for n>=1, a(n+1) is the number of (n+2)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007
Equals row sums of triangle A152230. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 29 2008]
a(n)= number of weak compositions of n with exeactly 2 parts are equal 0. [From Milan R. Janjic (agnus(AT)blic.net), Jun 27 2010]
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LINKS
| Milan Janjic, Two Enumerative Functions
Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) =(n+2)*(n+7)*2^(n-4) for n>0
a(n)=sum{k=0..floor((n+2)/2), C(n+2, 2k)k(k+1)/2 } - Paul Barry (pbarry(AT)wit.ie), May 15 2003
Binomial transform of quarter squares A002620 (without leading zeros). - Paul Barry (pbarry(AT)wit.ie), May 27 2003
a(n)=sum{k=0..n, C(n, k)Floor((k+2)^2/4) } - Paul Barry (pbarry(AT)wit.ie), May 27 2003
a(0)=1, a(1)=3, a(2)=9, a(3)=25, a(n)=6*a(n-1)-12*a(n-2)+8*a(n-3) [From Harvey P. Dale, Oct 17 2011]
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MATHEMATICA
| CoefficientList[ Series[(1 - x)^3/(1 - 2x)^3, {x, 0, 28}], x] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 28 2005)
Join[{1}, LinearRecurrence[{6, -12, 8}, {3, 9, 25}, 40]] (* From Harvey P. Dale, Oct 17 2011 *)
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CROSSREFS
| Cf. A045623. A diagonal of A058395.
Cf. A001793.
A152230 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 29 2008]
Sequence in context: A002064 A129589 A096322 * A006809 A081663 A181383
Adjacent sequences: A058393 A058394 A058395 * A058397 A058398 A058399
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Nov 24 2000
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EXTENSIONS
| More terms from Paul Barry (pbarry(AT)wit.ie), May 27 2003
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