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A112495
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Third column of triangle A112493 used for e.g.f.s of Stirling2 diagonals.
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4
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3, 25, 130, 546, 2037, 7071, 23436, 75328, 237127, 735813, 2260518, 6896046, 20933673, 63325051, 191088976, 575625900, 1731858075, 5206059585, 15640198410, 46966732090, 140996664733, 423191320215, 1269993390420
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OFFSET
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0,1
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10, -40, 82, -91, 52, -12).
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FORMULA
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a(n) = 3*a(n-1)+ (n+3)*(2^(n+2)-(n+3)), n>=1, a(0)=3.
G.f.: (3-5*x)/(((1-x)^3)*((1-2*x)^2)*(1-3*x)).
a(n) = 3^(n+4)/2 - (n+6)*2^(n+3) + n^2/2 + 9*n/2 + 21/2. - Vaclav Kotesovec, Jul 23 2021
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MATHEMATICA
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CoefficientList[Series[(3 - 5*x)/(((1 - x)^3)*((1 - 2*x)^2)*(1 - 3*x)), {x, 0, 50}], x] (* G. C. Greubel, Nov 13 2017 *)
Table[3^(n+4)/2 - (n+6)*2^(n+3) + n^2/2 + 9*n/2 + 21/2, {n, 0, 25}] (* Vaclav Kotesovec, Jul 23 2021 *)
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PROG
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(PARI) x='x+O('x^50); Vec((3-5*x)/(((1-x)^3)*((1-2*x)^2)*(1-3*x))) \\ G. C. Greubel, Nov 13 2017
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CROSSREFS
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Cf. A000295 (second column).
Column k=2 of A124324 (shifted).
Sequence in context: A215773 A099868 A243228 * A034578 A265874 A144646
Adjacent sequences: A112492 A112493 A112494 * A112496 A112497 A112498
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Oct 14 2005
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STATUS
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approved
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