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A112496 Fourth column of triangle A112493 used for e.g.f.s of Stirling2 diagonals. 3
15, 210, 1750, 11368, 63805, 325930, 1561516, 7150000, 31682651, 137031986, 582035714, 2438479592, 10109790809, 41579014154, 169946747160, 691299506640, 2801567046135, 11320801495410, 45642930545070, 183698923750440 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 13:31 EDT 2021. Contains 347563 sequences. (Running on oeis4.)