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A051798
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a(n) = (n+1)*(n+2)*(n+3)*(9n+4)/24.
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6
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1, 13, 55, 155, 350, 686, 1218, 2010, 3135, 4675, 6721, 9373, 12740, 16940, 22100, 28356, 35853, 44745, 55195, 67375, 81466, 97658, 116150, 137150, 160875, 187551, 217413, 250705, 287680, 328600, 373736, 423368, 477785, 537285
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OFFSET
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0,2
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COMMENTS
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-8.
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LINKS
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FORMULA
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a(n) = C(n+3, 3)*(9*n+4)/4.
G.f.: (1+8*x)/(1-x)^5.
a(0)=1, a(1)=13, a(2)=55, a(3)=155, a(4)=350, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Aug 19 2012
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MATHEMATICA
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Table[(n+1)(n+2)(n+3)(9n+4)/24, {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 13, 55, 155, 350}, 40] (* Harvey P. Dale, Aug 19 2012 *)
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PROG
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CROSSREFS
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Cf. A093644 ((9, 1) Pascal, column m=4).
Cf. A220212 for a list of sequences produced by the convolution of the natural numbers with the k-gonal numbers.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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