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A075922
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Third column of triangle A075502.
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2
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1, 42, 1225, 30870, 722701, 16235562, 355888225, 7683656190, 164302593301, 3491636199282, 73902587019625, 1560051480424710, 32874455072382301, 691950889177526202, 14553192008156093425, 305928163614832076430
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The e.g.f. given below is sum(A075513(3,m)*exp(7*(m+1)*x),m=0..2)/2!.
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FORMULA
| a(n)=A075502(n+3, 3)=(7^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).
a(n)= (7^n-8*14^n+9*21^n)/2.
G.f.: 1/product(1-7*k*x, k=1..3).
E.g.f.: diff((((exp(7*x)-1)/7)^3)/3!, x$3) = (exp(7*x)-8*exp(14*x)+9*exp(21*x))/2!.
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CROSSREFS
| Cf. A075921, A075923.
Sequence in context: A004373 A001778 A111780 * A077123 A121974 A096048
Adjacent sequences: A075919 A075920 A075921 * A075923 A075924 A075925
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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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