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Search: id:A107841
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| A107841 |
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Series reversion of x(1-3x)/(1-x). |
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+0
6
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| 1, 2, 10, 62, 430, 3194, 24850, 199910, 1649350, 13879538, 118669210, 1027945934, 9002083870, 79568077034, 708911026210, 6359857112438, 57403123415350, 520895417047010, 4749381474135850, 43489017531266654, 399755692955359630
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In general the series reversion of x(1-r*x)/(1-x) has g.f. (1+x-sqrt(1+2*(1-2*r)*x+x^2))/(2*r) and general term given by a(n)=(1/(n+1))sum{k=0..n, C(n+1,k)C(2n-k,n)(-1)^k*r^(n-k)}; a(n)=(1/(n+1))sum{k=0..n, C(n+1,k+1)C(n+k,k)(-1)^(n-k)*r^k}; a(n)=sum{k=0..n, (1/(k+1))*C(n,k)C(n+k,k)(-1)^(n-k)*r^k}; a(n)=sum{k=0..n, A088617(n,k)*(-1)^(n-k)*r^k}.
Hankel transform of this sequence is 6^C(n+1,2) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2007
The Hankel transform of this sequence is 6^C(n+1,2) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 05 2007
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FORMULA
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G.f.: (1+x-sqrt(1-10x+x^2))/(6x); a(n)=(1/(n+1))sum{k=0..n, C(n+1, k)C(2n-k, n)(-1)^k*3^(n-k)}; a(n)=(1/(n+1))sum{k=0..n, C(n+1, k+1)C(n+k, k)(-1)^(n-k)*3^k}; a(n)=sum{k=0..n, (1/(k+1))*C(n, k)C(n+k, k)(-1)^(n-k)*3^k}; a(n)=sum{k=0..n, A088617(n, k)*(-1)^(n-k)*3^k}.
a(n) = Sum_{k>=0} A086810(n, k)*2^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 26 2005
a(n)=(2/3)*A103210(n) for n>0 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2007
a(n)=(2/3)*A103210(n) for n>0 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 05 2007
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CROSSREFS
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Cf. A001003.
Sequence in context: A052600 A092165 A107026 this_sequence A141140 A129130 A078531
Adjacent sequences: A107838 A107839 A107840 this_sequence A107842 A107843 A107844
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 24 2005
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