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A053464 a(n) = n*5^(n-1). 14
0, 1, 10, 75, 500, 3125, 18750, 109375, 625000, 3515625, 19531250, 107421875, 585937500, 3173828125, 17089843750, 91552734375, 488281250000, 2593994140625, 13732910156250, 72479248046875, 381469726562500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

With a different offset, number of n-permutations of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly one u. - Zerinvary Lajos, Dec 28 2007

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

F. Ellermann, Illustration of binomial transforms

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 756

Index entries for linear recurrences with constant coefficients, signature (10,-25).

FORMULA

a(n) = Sum_(k=0..n, 5^(n-k)*binomial(n-k+1, k)*binomial(1, (k+1)/2)*(1-(-1)^k)/2 ). - Paul Barry, Oct 15 2004

a(n) = 10*a(n-1) - 25*a(n-2); n>1; a(0)=0, a(1)=1.

Fourth binomial transform of n (starting 0, 1, 10...) Convolution of powers of 5.

G.f.: x/(1-5*x)^2; E.g.f.: x*exp(5*x). - Paul Barry, Jul 22 2003

a(n) = - 25^n * a(-n) for all n in Z. - Michael Somos, Jun 26 2017

MATHEMATICA

Join[{a=0, b=1}, Table[c=10*b-25*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)

Table[n*5^(n-1), {n, 0, 20}] (* or *) LinearRecurrence[{10, -25}, {0, 1}, 30] (* Harvey P. Dale, Jul 22 2014 *)

PROG

(PARI) {a(n) = n*5^(n-1)}; /* Michael Somos, Sep 12 2005 */

(Sage) [lucas_number1(n, 10, 25) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 26 2009

(MAGMA) [n*(5^(n-1)): n in [0..30]]; // Vincenzo Librandi, Jun 09 2011

CROSSREFS

Cf. A002697, A027471, A001787.

Sequence in context: A027203 A291003 A305784 * A111998 A026935 A110127

Adjacent sequences:  A053461 A053462 A053463 * A053465 A053466 A053467

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 13 2000

EXTENSIONS

More terms from James A. Sellers, Feb 02 2000

STATUS

approved

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Last modified June 20 19:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)