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A107231
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C(n+2,2)C(n,floor(n/2)).
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3
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1, 3, 12, 30, 90, 210, 560, 1260, 3150, 6930, 16632, 36036, 84084, 180180, 411840, 875160, 1969110, 4157010, 9237800, 19399380, 42678636, 89237148, 194699232, 405623400, 878850700, 1825305300, 3931426800, 8143669800, 17450721000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Third column of A107230. Related to the generalized pentagonal numbers A001318. The sequence 0,0,1,3,12,... is an inverse Chebyshev transform of 0,0,1,3,8,... (see A034828). This transform maps a g.f. g(x) to (1/sqrt(1-4x^2))g(c(x^2)). Thus A001318, as first differences of A034828, can be expressed in terms of A107231.
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FORMULA
| G.f.: (1+x)(1-sqrt(1-4x^2))^3(sqrt(1-4x^2)-4x^2+1)^2/(8x^4(1-4x^2)^(5/2)(sqrt(1-4x^2)+2x-1)^2); a(n)=sum{k=0..floor((n+2)/2), binomial(n+2, k)*A034828(n-2k)};
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CROSSREFS
| Sequence in context: A064181 A089143 A073952 * A131936 A009135 A131740
Adjacent sequences: A107228 A107229 A107230 * A107232 A107233 A107234
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 13 2005
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