A112495 Third column of triangle A112493 used for e.g.f.s of Stirling2 diagonals.

3, 25, 130, 546, 2037, 7071, 23436, 75328, 237127, 735813, 2260518, 6896046, 20933673, 63325051, 191088976, 575625900, 1731858075, 5206059585, 15640198410, 46966732090, 140996664733, 423191320215, 1269993390420

Offset

0,1

Links

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).

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

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

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 14 2005

Status

approved