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A062191 Row sums of signed triangle A062138 (generalized a=5 Laguerre). 3
1, 5, 29, 191, 1405, 11389, 100585, 958271, 9758009, 105258005, 1191424981, 13996923775, 168226145269, 2023185762701, 23353840650785, 232509328597439, 1131674305674865, -36251185098769499, -1837042409174409971 (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)^5.

a(n) = Sum_{m=0..n} (-1)^m*n!*binomial(n+5, n-m)/m!.

MATHEMATICA

Table[n!*LaguerreL[n, 5, 1], {n, 0, 20}] (* Vaclav Kotesovec, Feb 25 2014 *)

PROG

(PARI) { f=1; for (n=0, 100, if (n>1, f*=n); a=f*binomial(n+5, n); g=1; a+=sum(m=1, n, ((-1)^m)*f*binomial(n+5, n-m)/g*=m); write("b062191.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 02 2009

(PARI) x = 'x + O('x^30); Vec(serlaplace(exp(-x/(1-x))/(1-x)^5)) \\  G. C. Greubel, May 11 2018

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-x/(1-x))/(1-x)^5)); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 11 2018

CROSSREFS

Sequence in context: A078945 A113713 A142980 * A171267 A258314 A225030

Adjacent sequences:  A062188 A062189 A062190 * A062192 A062193 A062194

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Jun 19 2001

EXTENSIONS

Typo in first formula corrected by Vaclav Kotesovec, Feb 25 2014

STATUS

approved

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Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)