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A143749
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Series reversion of x * (1 - x) / (1 + 9*x).
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2
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0, 1, 10, 110, 1310, 16610, 221010, 3051510, 43357110, 630098810, 9324499610, 140046944510, 2129440330510, 32716182966610, 507115641523810, 7920881045935110, 124548017695545510, 1969917348711212010
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Hankel transform of a(n) is A143750. Hankel transform of a(n+1) is 10^C(n+1,2).
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FORMULA
| G.f.: (1-9*x-sqrt(1-22*x+81*x^2))/2.
a(n) = sum{k=0..n-1, C(n+k-1,2*k)*A000108(k)*9^(n-k-1)}.
a(n+1) = sum{k=0..n, C(2*n-k,k)*A000108(n-k)*9^k}.
a(n+1) = 0^n+(1/(n+0^n)) * sum{k=0..n, C(n,k)*C(n,k-1)*10^k};
a(n+1) = Sum_{k, 0<=k<=n} 10^k*A090181(n,k). [From Philippe DELEHAM, Oct 14 2008]
a(n) = 9 * a(n-1) + Sum_{k=1..n-1} a(k) * a(n-k) if n>1. - Michael Somos, Jul 23 2011
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EXAMPLE
| x + 10*x^2 + 110*x^3 + 1310*x^4 + 16610*x^5 + 221010*x^6 + 3051510*x^7 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<1, 0, A = vector(n); A[1] = 1; for( k=2, n, A[k] = 9 * A[k-1] + sum( j=1, k-1, A[j] * A[k-j])); A[n])} /* Michael Somos, Jul 23 2011 */
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CROSSREFS
| Cf. A143750.
Sequence in context: A105279 A057093 A055276 * A049398 A055530 A108487
Adjacent sequences: A143746 A143747 A143748 * A143750 A143751 A143752
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Aug 30 2008
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