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A094664
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Row sums of triangle A094344.
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3
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1, 1, 2, 7, 38, 286, 2756, 32299, 444998, 7038898, 125620652, 2495811814, 54618201884, 1305184303996, 33812846036552, 943878836768947, 28242424937855558, 901709392642750186
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k = 0..n} A094344(n, k).
From Gary W. Adamson, Jul 26 2011: (start) a(n) = upper left term in M^n, a(n+1) = sum of top row terms in M^n; M = the following infinite square production matrix:
1, 1, 0, 0, 0,...
1, 1, 3, 0, 0,...
1, 1, 1, 5, 0,...
1, 1, 1, 1, 7,...
... (end)
G.f.: 1/(1 - x/(1 - x/(1 - 3*x/(1 - 3*x/(1 - 5*x/(1 - 5*x/(1 - 7*x/(1 - 7*x/(1-...))))))))) (continued fraction). [From Paul D. Hanna, Sep 17 2011]
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EXAMPLE
| a(3) = 7, a(4) = 38, since top row of M^3 = (7, 7, 9, 15) with 38 = (7 + 7 + 9 + 15).
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PROG
| (PARI) {a(n)=local(CF=1+x*O(x^n)); for(k=0, n, CF=1/(1-(2*n-2*k+1)*x/(1-(2*n-2*k+1)*x*CF))); polcoeff(CF, n, x)} /* Paul D. Hanna */
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CROSSREFS
| Sequence in context: A114160 A145159 A084552 * A001858 A000366 A106211
Adjacent sequences: A094661 A094662 A094663 * A094665 A094666 A094667
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KEYWORD
| easy,nonn
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AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 06 2004
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