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

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003013 E.g.f. 1+x*exp(x)+x^2*exp(2*x). 3
 1, 1, 4, 15, 52, 165, 486, 1351, 3592, 9225, 23050, 56331, 135180, 319501, 745486, 1720335, 3932176, 8912913, 20054034, 44826643, 99614740, 220200981, 484442134, 1061158935, 2315255832, 5033164825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8,-25,38,-28,8). FORMULA a(0) = 1, a(n) = (n^2-n)2^n/4 + n. a(n) = A002999(n) - n = A001815(n) + n. - Ralf Stephan, Sep 02 2003 O.g.f 1+x*(-1+4*x-8*x^2+6*x^3) ) / ( (x-1)^2*(2*x-1)^3 ). - R. J. Mathar, Mar 22 2011 a(0)=1, a(1)=1, a(2)=4, a(3)=15, a(4)=52, a(5)=165, a(n)= 8*a(n-1)- 25*a(n-2)+ 38*a(n-3)-28*a(n-4)+8*a(n-5) [From Harvey P. Dale, Nov 01 2011] MATHEMATICA With[{nn=30}, CoefficientList[Series[1+x Exp[x]+x^2 Exp[2x], {x, 0, nn}], x] Range[0, nn]!] (* or *) Join[{1}, LinearRecurrence[{8, -25, 38, -28, 8}, {1, 4, 15, 52, 165}, 30]] (* Harvey P. Dale, Nov 01 2011 *) PROG (PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 8, -28, 38, -25, 8]^n*[1; 1; 4; 15; 52])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020 CROSSREFS Cf. A048482, A001787, A005183. Sequence in context: A107307 A240365 A005492 * A117202 A291011 A137213 Adjacent sequences:  A003010 A003011 A003012 * A003014 A003015 A003016 KEYWORD nonn,easy AUTHOR 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 November 28 13:18 EST 2020. Contains 338724 sequences. (Running on oeis4.)