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A075922
Third column of triangle A075502.
2
1, 42, 1225, 30870, 722701, 16235562, 355888225, 7683656190, 164302593301, 3491636199282, 73902587019625, 1560051480424710, 32874455072382301, 691950889177526202, 14553192008156093425, 305928163614832076430
OFFSET
0,2
COMMENTS
The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(7*(m+1)*x)/2!.
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_{k=1..3} (1 - 7*k*x).
E.g.f.: (d^3/dx^3)(((exp(7*x)-1)/7)^3)/3! = (exp(7*x) - 8*exp(14*x) + 9*exp(21*x))/2!.
CROSSREFS
Sequence in context: A004373 A001778 A111780 * A230939 A331858 A331805
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 02 2002
STATUS
approved