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A038845
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3-fold convolution of A000302 (powers of 4).
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21
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1, 12, 96, 640, 3840, 21504, 114688, 589824, 2949120, 14417920, 69206016, 327155712, 1526726656, 7046430720, 32212254720, 146028888064, 657129996288, 2937757630464, 13056700579840, 57724360458240, 253987186016256
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also convolution of A002802 with A000984 (central binomial coefficients)
With a different offset, number of n-permutations of 5 objects u, v, w, z, x with repetition allowed, containing exactly two u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 29 2007
Also convolution of A000302 with A002697, also convolution of A002457 with itself. [From Rui Duarte, Oct 08 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
| a(n) = (n+2)*(n+1)*2^(2*n-1); G.f. 1/(1-4*x)^3.
a(n) = sum( a+b+c+d+e+f=n, f(a)*f(b)*f(c)*f(d)*f(e)*f(f)) with f(n)=A000984(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 22 2004
a(n) = binomial(n+2,n) * 4^n. [From Rui Duarte, Oct 08 2011]
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MAPLE
| seq(n*(n-1)*4^(n-2)/2, n=2..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
seq(seq(binomial(i, j)*4^(i-2), j =i-2), i=2..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2007
seq(seq(binomial(i+1, j)*4^(i-1), j =i-1), i=1..21); # - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 29 2007
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PROG
| (Other) SAGE: [lucas_number2(n, 4, 0)*binomial(n, 2)/2^4 for n in xrange(2, 26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 11 2009]
(MAGMA) [4^n*Binomial(n+2, 2): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011
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CROSSREFS
| Cf. A000302, A002802, A000984.
Cf. A052780.
Cf. A038231.
Cf. A038231.
Sequence in context: A121627 A138162 A073392 * A204623 A155620 A059375
Adjacent sequences: A038842 A038843 A038844 * A038846 A038847 A038848
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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