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!)
 A001908 E.g.f. exp(-x)/(1-5*x). (Formerly M3677 N1500) 5
 1, 4, 41, 614, 12281, 307024, 9210721, 322375234, 12895009361, 580275421244, 29013771062201, 1595757408421054, 95745444505263241, 6223453892842110664, 435641772498947746481, 32673132937421080986074, 2613850634993686478885921, 222177303974463350705303284 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 83. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 0..100 FORMULA E.g.f.: A(x) = exp(-x)/(1-5x) satisfies (1-5x)A' - (4+5x)A = 0. - Gheorghe Coserea, Aug 06 2015 a(n+1) = (5n+4) a(n) + 5n a(n-1). - Gheorghe Coserea, Aug 06 2015 a(n) = 5^n*exp(-1/5)*Gamma(n+1,-1/5), where Gamma is the incomplete Gamma function. - Robert Israel, Aug 06 2015 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (5*k - 1) * a(n-k). - Ilya Gutkovskiy, Jan 17 2020 MAPLE f:= gfun:-rectoproc({a(n+1) = (5*n+4)* a(n) + 5*n*a(n-1), a(0)=1, a(1)=4}, a(n), remember): seq(f(n), n=0..30); # Robert Israel, Aug 06 2015 MATHEMATICA nn = 20; Range[0, nn]! CoefficientList[Series[Exp[-x]/(1 - 5 x), {x, 0, nn}], x] (* T. D. Noe, Aug 17 2012 *) PROG (PARI) x='x+O('x^33); Vec(serlaplace(exp(-x)/(1-5*x))) \\ Gheorghe Coserea, Aug 06 2015 CROSSREFS Column k=5 of A320032. Sequence in context: A134277 A085340 A230251 * A270703 A192547 A006129 Adjacent sequences:  A001905 A001906 A001907 * A001909 A001910 A001911 KEYWORD nonn 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 September 24 14:46 EDT 2020. Contains 337321 sequences. (Running on oeis4.)