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A160568
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Diagonal sums of number triangle [k<=n]*C(n,2n-2k)3^(n-k)A000108(n-k).
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1
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1, 0, 1, 3, 1, 9, 19, 18, 91, 165, 271, 990, 1765, 3843, 11467, 21630, 53299, 140724, 287119, 736101, 1818235, 3982044, 10225117, 24521409, 56584243, 143641017, 341948179, 816095982, 2045559205, 4888806237, 11897144767, 29540684052
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Hankel transform is A160569(n+1).
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FORMULA
| G.f.: (1-x^2-sqrt(1-2x^2-12x^3+x^4))/(6*x^3);
G.f.: 1/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-... (continued fraction).
a(n)=sum{k=0..floor(n/2), C(n-k,2n-4k)*3^(n-2k)*A000108(n-2k)};
a(n)=sum{k=0..n, C(n-k/2,2(n-k))*3^(n-k)*A000108(n-k)*(1+(-1)^k)/2};
a(n)=sum{k=0..n, C((n+k)/2,2k)*3^k*A000108(k)(1+(-1)^(n-k))/2}.
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CROSSREFS
| Cf.: A025250, A160565.
Sequence in context: A111568 A121489 A118793 * A157403 A105951 A038202
Adjacent sequences: A160565 A160566 A160567 * A160569 A160570 A160571
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 19 2009
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