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 A038845 3-fold convolution of A000302 (powers of 4). 33
 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; text; internal format)
 OFFSET 0,2 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, Dec 29 2007 Also convolution of A000302 with A002697, also convolution of A002457 with itself. - Rui Duarte, Oct 08 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 Index entries for linear recurrences with constant coefficients, signature (12,-48,64). 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). - Philippe Deléham, Jan 22 2004 a(n) = binomial(n+2,n) * 4^n. - Rui Duarte, Oct 08 2011 E.g.f.: (1 + 8*x + 8*x^2)*exp(4*x). - G. C. Greubel, Jul 20 2019 From Amiram Eldar, Jan 05 2022: (Start) Sum_{n>=0} 1/a(n) = 8 - 24*log(4/3). Sum_{n>=0} (-1)^n/a(n) = 40*log(5/4) - 8. (End) MAPLE seq((n+2)*(n+1)*4^n/2, n=0..30); # Zerinvary Lajos, Apr 25 2007 MATHEMATICA Table[4^n*Binomial[n+2, n], {n, 0, 30}] (* G. C. Greubel, Jul 20 2019 *) PROG (Sage) [4^(n-2)*binomial(n, 2) for n in range(2, 30)] # Zerinvary Lajos, Mar 11 2009 (MAGMA) [4^n*Binomial(n+2, 2): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011 (PARI) a(n)=(n+2)*(n+1)<<(2*n-1) \\ Charles R Greathouse IV, Aug 21 2015 (GAP) List([0..30], n-> 4^n*Binomial(n+2, n) ); # G. C. Greubel, Jul 20 2019 CROSSREFS Cf. A000302, A000984, A002802, A038231, A052780. Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), this sequence (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), A081142 (q=12), A027476 (q=15). Sequence in context: A138162 A264418 A073392 * A204623 A270568 A223151 Adjacent sequences:  A038842 A038843 A038844 * A038846 A038847 A038848 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)