A001908 E.g.f. exp(-x)/(1-5*x). (Formerly M3677 N1500)

1, 4, 41, 614, 12281, 307024, 9210721, 322375234, 12895009361, 580275421244, 29013771062201, 1595757408421054, 95745444505263241, 6223453892842110664, 435641772498947746481, 32673132937421080986074, 2613850634993686478885921, 222177303974463350705303284

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 * A367836 A367846 A270703

Adjacent sequences: A001905 A001906 A001907 * A001909 A001910 A001911

Keyword

nonn

Author

N. J. A. Sloane

Status

approved