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A104532
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Expansion of (1+sqrt(1-4x))/(6sqrt(1-4x)-4).
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1
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1, 5, 35, 250, 1795, 12910, 92910, 668820, 4815075, 34667110, 249598330, 1797091180, 12938997710, 93160575500, 670755400700, 4829436210600, 34771931021475, 250357867996950, 1802576519933250, 12978550465880700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse (1/(1-x),x(1-x))) to 6^n. In general, (1+sqrt(1-4x))(k*sqrt(1-4x)-(k-2)) results from applying the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse of (1/(1-x),x(1-x))) to k^n. We then have a(n)=0^n+sum{i=0..n, (k-1)^(i+1)*C(2n-1,n-i-1)2(i+1)/(n+i+1)}.
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FORMULA
| a(n)=0^n+sum{k=0..n, 5^(k+1)*C(2n-1, n-k-1)2(k+1)/(n+k+1)
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MATHEMATICA
| CoefficientList[Series[(1+Sqrt[1-4x])/(6Sqrt[1-4x]-4), {x, 0, 20}], x] (* From Harvey P. Dale, Apr 11 2011 *)
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CROSSREFS
| Cf. A088218, A067336, A076025, 104530, 104531.
Sequence in context: A155127 A193577 A196661 * A180900 A087630 A084135
Adjacent sequences: A104529 A104530 A104531 * A104533 A104534 A104535
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 12 2005
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