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A062109
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Expansion of ((1-x)/(1-2*x))^4.
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13
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1, 4, 14, 44, 129, 360, 968, 2528, 6448, 16128, 39680, 96256, 230656, 546816, 1284096, 2990080, 6909952, 15859712, 36175872, 82051072, 185139200, 415760384, 929562624, 2069889024, 4591714304, 10150215680, 22364028928
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OFFSET
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0,2
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COMMENTS
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If X_1,X_2,...,X_n are 2-blocks of a (2n+4)-set X then, for n >= 1, a(n+1) is the number of (n+3)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 23 2007
If the offset here is set to zero, the binomial transform of A006918. - R. J. Mathar, Jun 29 2009
a(n) is the number of weak compositions of n with exactly 3 parts equal to 0. - Milan Janjic, Jun 27 2010
Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)^4; see A291000. - Clark Kimberling, Aug 24 2017
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LINKS
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FORMULA
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a(n) = (n+5)*(n^2 + 13*n + 18)*2^(n-5)/3, with a(0)=1.
a(n) = Sum_{k<n} a(k) + A058396(n).
G.f.: (1-x)^4/(1-2*x)^4.
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MAPLE
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seq(coeff(series(((1-x)/(1-2*x))^4, x, n+1), x, n), n=0..30); # Muniru A Asiru, Jul 01 2018
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MATHEMATICA
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CoefficientList[Series[(1 - x)^4/(1 - 2 x)^4, {x, 0, 26}], x] (* Michael De Vlieger, Jul 01 2018 *)
LinearRecurrence[{8, -24, 32, -16}, {1, 4, 14, 44, 129}, 30] (* Harvey P. Dale, Sep 02 2022 *)
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PROG
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(PARI) a(n)=if(n<1, n==0, (n+5)*(n^2+13*n+18)*2^n/96)
(PARI) { a=1; for (n=0, 200, if (n, a=(n + 5)*(n^2 + 13*n + 18)*2^n/96); write("b062109.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 01 2009
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(((1-x)/(1-2*x))^4)); // G. C. Greubel, Oct 16 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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