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 A082138 A transform of C(n,3). 10
 1, 4, 20, 80, 280, 896, 2688, 7680, 21120, 56320, 146432, 372736, 931840, 2293760, 5570560, 13369344, 31752192, 74711040, 174325760, 403701760, 928514048, 2122317824, 4823449600, 10905190400, 24536678400, 54962159616, 122607894528 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Fourth row of number array A082137. C(n,3) has e.g.f. (x^3/3!)exp(x). The transform averages the binomial and inverse binomial transforms. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16). FORMULA a(n) = (2^(n-1)+0^n/2)C(n+3, n) = sum{j=0..n, C(n+3, j+3)C(j+3, 3)(1+(-1)^j)/2 }. G.f.: (1-4x+12x^2-16x^3+8x^4)/(1-2x)^4. E.g.f.: (x^3/3!)exp(x)cosh(x) (preceded by 3 zeros). a(n) = ceil(binomial(n+3,3)*2^(n-1)). - Zerinvary Lajos, Nov 01 2006 EXAMPLE a(0)=(2^(-1)+0^0/2)C(3,0)=2*(1/2)=1 (use 0^0=1). MAPLE [seq (ceil(binomial(n+3, 3)*2^(n-1)), n=0..26)]; # Zerinvary Lajos, Nov 01 2006 PROG (MAGMA) [(Ceiling(Binomial(n+3, 3)*2^(n-1))) : n in [0..30]]; // Vincenzo Librandi, Sep 22 2011 CROSSREFS Cf. A080929, A082139, A082140, A082141, A080951, A057711. Sequence in context: A295116 A303508 A258627 * A074358 A255050 A292540 Adjacent sequences:  A082135 A082136 A082137 * A082139 A082140 A082141 KEYWORD easy,nonn AUTHOR Paul Barry, Apr 06 2003 STATUS approved

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Last modified May 25 04:50 EDT 2019. Contains 323539 sequences. (Running on oeis4.)