The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A062192 Row sums of unsigned triangle A062138 (generalized a=5 Laguerre). 6
 1, 7, 57, 529, 5509, 63591, 805597, 11109337, 165625929, 2654025319, 45481765921, 829903882017, 16062421776397, 328634683136839, 7086337847838789, 160604998959958441, 3816483607166825617 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..441 (terms 0..100 from Harry J. Smith) FORMULA E.g.f.: exp(x/(1-x))/(1-x)^6. a(n) = Sum_{m=0..n} n!*binomial(n+5, n-m)/m!. a(n) = (2*n+5)*a(n-1) - (n-1)*(n+4)*a(n-2). - Vaclav Kotesovec, Oct 11 2012 a(n) ~ exp(2*sqrt(n)-n-1/2)*n^(n+11/4)/sqrt(2). - Vaclav Kotesovec, Oct 11 2012 a(n) = n!*LaguerreL(n, 5, -1). - G. C. Greubel, Mar 10 2021 MAPLE A062192:= n -> n!*simplify(LaguerreL(n, 5, -1), 'LaguerreL'); seq(A062192(n), n = 0 .. 30); # G. C. Greubel, Mar 10 2021 MATHEMATICA Table[Sum[n! Binomial[n+5, n-m]/m!, {m, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Apr 11 2012 *) 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, f*binomial(n+5, n-m)/g*=m); write("b062192.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 02 2009 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(x/(1-x))/(1-x)^6)) \\ G. C. Greubel, Feb 06 2018 (PARI) a(n) = vecsum(apply(abs, Vec(n!*pollaguerre(n, 5)))); \\ Michel Marcus, Feb 06 2021 (MAGMA) [Factorial(n)*(&+[Binomial(n+5, n-m)/Factorial(m): m in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018 (Sage) [factorial(n)*gen_laguerre(n, 5, -1) for n in (0..30)] # G. C. Greubel, Mar 10 2021 CROSSREFS Cf. A062138, A216294. Sequence in context: A147689 A248168 A176733 * A122649 A051846 A231540 Adjacent sequences:  A062189 A062190 A062191 * A062193 A062194 A062195 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jun 19 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)