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A075921
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Second column of triangle A075502.
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2
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1, 21, 343, 5145, 74431, 1058841, 14941423, 210003465, 2945813311, 41281739961, 578226834703, 8097153012585, 113373983463391, 1587332657497881, 22223335428043183, 311131443554114505
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OFFSET
| 0,2
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COMMENTS
| The e.g.f. given below is sum(A075513(2,m)*exp(7*(m+1)*x),m=0..1).
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FORMULA
| a(n)=A075502(n+2, 2)=(7^n)*S2(n+2, 2) with S2(n, m) := A008277(n, m) (Stirling2).
a(n)=-7^n+2*14^n.
G.f.: 1/((1-7*x)*(1-14*x)).
E.g.f.: diff((((exp(7*x)-1)/7)^2)/2!, x$2) = -exp(7*x)+2*exp(14*x).
a(0)=1, a(1)=21, a(n)=21a(n-1)-98a(n-2)[From Harvey P. Dale, Apr 30 2011]
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MATHEMATICA
| Table[-7^n+2 14^n, {n, 0, 20}] (* or *) LinearRecurrence[{21, -98}, {1, 21}, 20] (* From Harvey P. Dale, Apr 30 2011 *)
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CROSSREFS
| Cf. A000420 (first column), A075922.
Sequence in context: A020311 A068705 A144864 * A201878 A184289 A192093
Adjacent sequences: A075918 A075919 A075920 * A075922 A075923 A075924
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 02, 2002
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