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A128709
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O.g.f.: A(x) = 1/(1-1*x/(1-3*x/(1-5*x/(1-7*x/(1-...-(2n-1)*x/(1-...)))))) (continued fraction).
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5
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1, 1, 4, 31, 364, 5746, 113944, 2719291, 75843724, 2420160286, 86941080904, 3471911602006, 152562875644984, 7315129181611876, 380045172886143664, 21266347877729314771, 1275148311699896290444, 81563275661324271278566
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Hankel transform is A168440. [From Paul Barry (pbarry(AT)wit.ie), Nov 25 2009]
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FORMULA
| a(n)=Sum_{k, 0<=k<=n}(-1)^k*2^(n-k)*A053979(n,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 24 2007
a(n)=Sum_{k, 0<=k<=n}A094344(n,k)*3^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 27 2007
G.f.: 1/(1-x-3x^2/(1-8x-35x^2/(1-16x-99x^2/(1-24x-195x^2/(1-32x-323x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Nov 25 2009]
a(n) = top left term of M^n, n>0; M = the infinite square production matrix:
1, 3, 0, 0,...
1, 3, 5, 0,...
1, 3, 5, 7,...
...
Also, a(n+1) = sum of top row terms of M^n. Example: top row of M^3 = (31, 93, 135, 105, 0, 0, 0,...), where a(3) = 31 and a(4) = 364 = (31 + 93 + 135 + 105). - Gary W. Adamson, Jul 14 2011
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EXAMPLE
| G.f.: A(x) = 1 + x + 4x^2 + 31x^3 + 364x^4 + 5746x^5 +...;
A(x) = 1/(1 - x*(1 + 3x + 24x^2 + 297x^3 + 4896x^4 +...));
A(x) = 1/(1 - x/(1 - 3x*(1 + 5x + 60x^2 + 1035x^3 + 22500x^4+...)));
A(x) = 1/(1 - x/(1 - 3x/(1 - 5x*(1 + 7x + 112x^2 + 2485x^3 +...)))).
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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*CF)); polcoeff(CF, n, x)}
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CROSSREFS
| Sequence in context: A086677 A016036 A000314 * A138860 A198865 A145087
Adjacent sequences: A128706 A128707 A128708 * A128710 A128711 A128712
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 23 2007
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