A112497 Fifth column of triangle A112493 used for e.g.f.s of Stirling2 diagonals.

105, 2205, 26775, 247555, 1939630, 13609310, 88346258, 541831290, 3184396215, 18114492851, 100467071393, 546227989621, 2923225973476, 15447710150460, 80807432442660, 419245751359380, 2160664798858005, 11075023230179865

Offset: 0

Author

Wolfdieter Lang, Oct 14 2005

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (35, -560, 5432, -35714, 168542, -589632, 1556776, -3126949, 4777591, -5506936, 4703032, -2881136, 1195632, -300672, 34560).

Crossrefs

Cf. A112496 (fourth column).

Column k=4 of A124324 (shifted).

Programs

Mathematica

CoefficientList[Series[(105 - 1470*x + 8400*x^2 - 25130*x^3 + 41615*x^4 - 36280*x^5 + 13048*x^6)/Product[(1 - j*x)^(6 - j), {j, 1, 5}], {x, 0, 50}], x] (* G. C. Greubel, Nov 13 2017 *)

PARI

x='x+O('x^50); Vec((105 -1470*x +8400*x^2 -25130*x^3 +41615*x^4 -36280*x^5 +13048*x^6)/((1-x)^5*(1-2*x)^4*(1-3*x)^3*(1-4*x)^2*(1-5*x))) \\ G. C. Greubel, Nov 13 2017

Formula

G.f.: (105-1470*x+8400*x^2-25130*x^3+41615*x^4-36280*x^5+13048*x^6) / product((1-j*x)^(6-j), j=1..5).

a(n) = 5*a(n-1) + (n+7)*A112496(n).