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A054340 10-fold convolution of A000302 (powers of 4). 3
1, 40, 880, 14080, 183040, 2050048, 20500480, 187432960, 1593180160, 12745441280, 96865353728, 704475299840, 4931327098880, 33381291130880, 219362770288640, 1403921729847296, 8774510811545600, 53679360258867200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

With a different offset, number of n-permutations (n>=9) of 5 objects: u, v, z, x, y with repetition allowed, containing exactly nine (9) u's. - Zerinvary Lajos, Jul 02 2008

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

FORMULA

a(n) = binomial(n+9, 9)*4^n.

G.f.: 1/(1 - 4*x)^10.

a(n) = A054335(n+19, 19).

E.g.f.: (2^7/9!)*(2835 +102060*x +816480*x^2 +2540160*x^3 +3810240*x^4 +3048192*x^5 +1354752*x^6 +331776*x^7 +41472*x^8 +2048*x^9)*exp(4*x).

MAPLE

seq(binomial(n+9, 9)*4^n, n=0..20); # Zerinvary Lajos, Jul 02 2008

MATHEMATICA

Table[4^n*Binomial[n+9, 9], {n, 0, 20}] (* G. C. Greubel, Jul 21 2019 *)

PROG

(Sage) [lucas_number2(n, 4, 0)*binomial(n, 9)/2^18 for n in xrange(9, 29)] # Zerinvary Lajos, Mar 11 2009

(MAGMA) [4^n*Binomial(n+9, 9): n in [0..20]]; // Vincenzo Librandi, Oct 15 2011

(PARI) vector(20, n, n--; 4^n*binomial(n+9, 9)) \\ G. C. Greubel, Jul 21 2019

(GAP) List([0..20], n-> 4^n*Binomial(n+9, 9)); # G. C. Greubel, Jul 21 2019

CROSSREFS

Cf. A000302, A054335.

Sequence in context: A247411 A250986 A190825 * A271030 A013350 A013346

Adjacent sequences:  A054337 A054338 A054339 * A054341 A054342 A054343

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang, Mar 13 2000

STATUS

approved

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Last modified November 18 07:22 EST 2019. Contains 329252 sequences. (Running on oeis4.)