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Search: id:A075906
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| 1, 84, 4158, 158760, 5182947, 152457228, 4166544096, 107883135360, 2681751885813, 64597295294532, 1518037879508514, 34979886546859800, 793401360863472999, 17766424516726033596, 393690756719422620612
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OFFSET
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0,2
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COMMENT
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The e.g.f. given below is sum(A075513(7,m)*exp(3*(m+1)*x),m=0..6)/6!.
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FORMULA
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a(n)=A075498(n+7, 7)=(3^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
a(n)= sum(A075513(7, m)*((m+1)*3)^n, m=0..6)/6!.
G.f.: 1/product(1-3*k*x, k=1..7).
E.g.f.: diff((((exp(3*x)-1)/3)^7)/7!, x$7) = (exp(3*x)-384*exp(6*x)+10935*exp(9*x)-81920*exp(12*x)+234375*exp(15*x)-279936*exp(18*x)+117649*exp(21*x))/6!.
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CROSSREFS
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Cf. A075516.
Adjacent sequences: A075903 A075904 A075905 this_sequence A075907 A075908 A075909
Sequence in context: A017747 A143402 A004379 this_sequence A075909 A132052 A097840
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 02, 2002
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