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A119371
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G.f. satisfies: A(x) = (1+x) - x*(4+x)*A(x) + x*(3+2*x)*A(x)^2.
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7
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1, 0, 1, 2, 7, 23, 81, 293, 1087, 4110, 15783, 61387, 241329, 957400, 3828055, 15410651, 62410871, 254095382, 1039394147, 4269718110, 17606507789, 72852976317, 302403773303, 1258855723796, 5254253027485, 21983753239135
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Equals central terms of pendular trinomial triangle A119369.
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FORMULA
| G.f.: A(x) = (1+4*x+x^2 - sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x)))/(2*x*(3+2*x)). G.f.: A(x) = 1/(1+x - x*B(x)) = (1 + x*H(x))/(1+x) = 1 + x^2*F(x)/B(x), where B(x) is g.f. of A119370, H(x) is g.f. of A119372, F(x) is g.f. of A119375.
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EXAMPLE
| A(x) = 1 + x^2 + 2*x^3 + 7*x^4 + 23*x^5 + 81*x^6 + 293*x^7 +...
-x*(4+x)*A(x) = -4*x -x^2 -4*x^3 -9*x^4 -30*x^5 -99*x^6 -...
x*(3+2*x)*A(x)^2 = 3*x +2*x^2 +6*x^3 +16*x^4 +53*x^5 +180*x^6 +...
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PROG
| (PARI) {a(n)=polcoeff((2*(1+x))/(1+4*x+x^2+sqrt((1+4*x+x^2)^2-4*x*(1+x)*(3+2*x)+x*O(x^n))), n)}
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CROSSREFS
| Cf. A119369, A119370, A119372, A119373, A119374, A119375, A119376.
Sequence in context: A091514 A143629 A176287 * A151290 A047002 A127497
Adjacent sequences: A119368 A119369 A119370 * A119372 A119373 A119374
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 17 2006
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