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A054340
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10-fold convolution of A000302 (powers of 4).
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3
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1, 40, 880, 14080, 183040, 2050048, 20500480, 187432960, 1593180160, 12745441280, 96865353728, 704475299840, 4931327098880, 33381291130880, 219362770288640, 1403921729847296, 8774510811545600, 53679360258867200, 322076161553203200, 1898554215471513600
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history;
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (40,-720,7680,-53760,258048,-860160,1966080,-2949120,2621440,-1048576).
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FORMULA
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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).
From Amiram Eldar, Mar 27 2022: (Start)
Sum_{n>=0} 1/a(n) = 236196*log(4/3) - 4756383/70.
Sum_{n>=0} (-1)^n/a(n) = 14062500*log(5/4) - 43931373/14. (End)
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MAPLE
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seq(binomial(n+9, 9)*4^n, n=0..20); # Zerinvary Lajos, Jul 02 2008
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MATHEMATICA
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Table[4^n*Binomial[n+9, 9], {n, 0, 20}] (* G. C. Greubel, Jul 21 2019 *)
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PROG
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(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
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CROSSREFS
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Cf. A000302, A054335.
Sequence in context: A247411 A250986 A190825 * A271030 A013350 A013346
Adjacent sequences: A054337 A054338 A054339 * A054341 A054342 A054343
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang, Mar 13 2000
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STATUS
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approved
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