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A080609
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Binomial transform of central Delannoy numbers, i.e. binomial transform of A001850.
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0
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1, 4, 20, 112, 664, 4064, 25376, 160640, 1027168, 6618496, 42904960, 279503360, 1828222720, 11999226880, 78984381440, 521218322432, 3447059138048, 22840932997120, 151607254267904, 1007830488424448, 6708862677274624
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The Hankel transform (see A001906 for definition) of this sequence is A036442 : 1, 4, 32, 512, 16384, ... . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 03 2005
Coefficient of x^n in (1+4*x+2*x^2)^n - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Jan 17 2008
Number of paths from (0,0) to (n,0) using only steps U=(1,1), H=(1,0) and D=(1,-1), U can have 2 colors and H can have 4 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Jan 27 2008
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REFERENCES
| Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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FORMULA
| G.f.: 1 / Sqrt( 1 - 8 x + 8 x^2 ) = ( 1 - 8 x + 8 x^2 )^(-1/2) Formula: sum( binomial(n, k) d(k), k = 0 .. n ) where d(n) = central Delannoy number.
E.g.f.: exp(4*x)*BesselI(0, 2*sqrt(2)*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 21 2004
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MATHEMATICA
| Table[SeriesCoefficient[Series[1/Sqrt[1-8x+8x^2], {x, 0, n}], n], {n, 0, 12}]
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CROSSREFS
| Sequence in context: A153299 A081335 A136783 * A003645 A081085 A192624
Adjacent sequences: A080606 A080607 A080608 * A080610 A080611 A080612
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KEYWORD
| easy,nonn
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AUTHOR
| Emanuele Munarini (munarini(AT)mate.polimi.it), Feb 26 2003
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