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Search: id:A119370
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| A119370 |
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G.f. satisfies: A(x) = 1 + x*A(x)^2 + x^2*(A(x)^2 - A(x)). |
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+0
10
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| 1, 1, 2, 6, 19, 64, 225, 816, 3031, 11473, 44096, 171631, 675130, 2679728, 10719237, 43168826, 174885089, 712222799, 2914150406, 11973792218, 49385167369, 204386777160, 848530495383, 3532844222611, 14747626307436, 61712139464939
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equals base sequence of pendular trinomial triangle A119369; iterated convolutions of this sequence with the central terms (A119371) generates all diagonals of A119369. For example: A119372 = A119370 * A119371; A119373 = A119370^2 * A119371.
Diagonal sums of number array A133336. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 09 2009]
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FORMULA
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G.f.: A(x) = ((1+x^2) - sqrt( (1+x^2)^2 - 4*x*(1+x) ))/(2*x*(1+x)). Equals the inverse binomial transform of A104547.
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EXAMPLE
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A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 64*x^5 + 225*x^6 + 816*x^7 +...
x*A(x)^2 = x + 2*x^2 + 5*x^3 + 16*x^4 + 54*x^5 + 190*x^6 + 690*x^7 +...
x^2*( A(x)^2 - A(x) ) = 1*x^3 + 3*x^4 + 10*x^5 + 35*x^6 + 126*x^7 +...
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PROGRAM
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(PARI) {a(n)=polcoeff(2/((1+x^2)+sqrt((1+x^2)^2-4*x*(1+x)+x*O(x^n))), n)}
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CROSSREFS
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Cf. A119369, A119371, A119372, A119373, A119374, A119375, A119376; A104547.
Sequence in context: A148468 A148469 A151283 this_sequence A069728 A150083 A047016
Adjacent sequences: A119367 A119368 A119369 this_sequence A119371 A119372 A119373
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KEYWORD
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nonn,new
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 16 2006
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