A112496 Fourth column of triangle A112493 used for e.g.f.s of Stirling2 diagonals.

15, 210, 1750, 11368, 63805, 325930, 1561516, 7150000, 31682651, 137031986, 582035714, 2438479592, 10109790809, 41579014154, 169946747160, 691299506640, 2801567046135, 11320801495410, 45642930545070, 183698923750440

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 (20, -175, 882, -2835, 6072, -8777, 8458, -5204, 1848, -288).

Formula

G.f.: (15-90*x+175*x^2-112*x^3)/((1-x)^4*(1-2*x)^3*(1-3*x)^2*(1-4*x)).

a(n) = 4*a(n-1) + (n+5)*A112495(n).

a(n) = 2^(2*n+11)/3- 3^(n+5)*(n+9)/2 + 2^(n+3)*(n^2 + 15*n + 58) - n^3/6 - 3*n^2 - 55*n/3 - 229/6. - Vaclav Kotesovec, Jul 23 2021

Mathematica

CoefficientList[Series[(15 - 90*x + 175*x^2 - 112*x^3)/((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^2*(1 - 4*x)), {x, 0, 50}], x] (* G. C. Greubel, Nov 13 2017 *)
Table[2^(2*n+11)/3- 3^(n+5)*(n+9)/2 + 2^(n+3)*(n^2 + 15*n + 58) - n^3/6 - 3*n^2 - 55*n/3 - 229/6, {n, 0, 25}] (* Vaclav Kotesovec, Jul 23 2021 *)

Prog

(PARI) x='x+O('x^50); Vec((15-90*x+175*x^2-112*x^3)/((1-x)^4*(1-2*x)^3*(1-3*x)^2*(1-4*x))) \\ G. C. Greubel, Nov 13 2017

Crossrefs

Cf. A112495 (third column).

Column k=3 of A124324 (shifted).

Sequence in context: A067560 A019553 A234249 * A000483 A162785 A076139

Adjacent sequences: A112493 A112494 A112495 * A112497 A112498 A112499

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 14 2005

Status

approved