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A054338 8-fold convolution of A000302 (powers of 4). 3
1, 32, 576, 7680, 84480, 811008, 7028736, 56229888, 421724160, 2998927360, 20392706048, 133479530496, 845370359808, 5202279137280, 31213674823680, 183120225632256, 1052941297385472, 5946021444059136, 33033452466995200, 180814687187763200, 976399310813921280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

With a different offset, number of n-permutations (n>=7) of 5 objects: u, v, z, x, y with repetition allowed, containing exactly seven (7) u's. - Zerinvary Lajos, Jun 23 2008

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (32,-448,3584,-17920,57344,-114688,131072,-65536).

FORMULA

a(n) = binomial(n+7, 7)*4^n.

G.f.: 1/(1-4*x)^8.

a(n) = A054335(n+15, 15).

E.g.f.: (315 + 8820*x + 52920*x^2 + 117600*x^3 + 117600*x^4 + 56448*x^5 + 12544*x^6 + 1024*x^7)*exp(4*x)/315. - G. C. Greubel, Jul 21 2019

From Amiram Eldar, Mar 27 2022: (Start)

Sum_{n>=0} 1/a(n) = 20412*log(4/3) - 88067/15.

Sum_{n>=0} (-1)^n/a(n) = 437500*log(5/4) - 292873/3. (End)

MAPLE

seq(binomial(n+7, 7)*4^n, n=0..20); # Zerinvary Lajos, Jun 23 2008

MATHEMATICA

Table[4^n*Binomial[n+7, 7], {n, 0, 20}] (* G. C. Greubel, Jul 21 2019 *)

PROG

(Magma) [4^n*Binomial(n+7, 7): n in [0..20]]; // Vincenzo Librandi, Oct 15 2011

(PARI) vector(20, n, n--; 4^n*binomial(n+7, 7)) \\ G. C. Greubel, Jul 21 2019

(GAP) List([0..20], n-> 4^n*Binomial(n+7, 7) ); # G. C. Greubel, Jul 21 2019

CROSSREFS

Cf. A000302, A054335.

Cf. A038231.

Sequence in context: A317009 A316874 A317602 * A234435 A010557 A022756

Adjacent sequences:  A054335 A054336 A054337 * A054339 A054340 A054341

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang, Mar 13 2000

STATUS

approved

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Last modified July 4 01:37 EDT 2022. Contains 355063 sequences. (Running on oeis4.)