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A062146 Row sums of signed triangle A062137 (generalized Laguerre, a=3). 3
1, 3, 11, 47, 225, 1159, 6067, 28419, 58433, -1390645, -35514309, -636045257, -10431927839, -167173905393, -2678202265885, -43236880758901, -703702453254783, -11485574113211501, -185707408082199317, -2901041900411825985 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..100

Index entries for sequences related to Laguerre polynomials

FORMULA

E.g.f.: exp(-x/(1-x))/(1-x)^4.

a(n) = sum(((-1)^m)*n!*binomial(n+3, n-m)/m!, m=0..n).

a(n) = (2*n+1)*a(n-1) - (n-1)*(n+2)*a(n-2). - Vaclav Kotesovec, Aug 01 2013

MATHEMATICA

Table[n!*LaguerreL[n, 3, 1], {n, 0, 20}] (* Vaclav Kotesovec, Aug 01 2013 *)

PROG

(PARI) { f=1; for (n=0, 100, if (n>1, f*=n); a=f*binomial(n+3, n); g=1; a+=sum(m=1, n, ((-1)^m)*f*binomial(n+3, n-m)/g*=m); write("b062146.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 02 2009

(PARI) x='x+O('x^30); Vec(exp(-x/(1-x))/(1-x)^4) \\ G. C. Greubel, May 11 2018

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-x/(1-x))/(1-x)^4)); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 11 2018

CROSSREFS

Sequence in context: A301409 A295539 A174347 * A216947 A090365 A035009

Adjacent sequences:  A062143 A062144 A062145 * A062147 A062148 A062149

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Jun 19 2001

STATUS

approved

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Last modified February 25 08:21 EST 2020. Contains 332221 sequences. (Running on oeis4.)