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 A042984 Number of n-dimensional partitions of 6. 6
 1, 11, 48, 140, 326, 657, 1197, 2024, 3231, 4927, 7238, 10308, 14300, 19397, 25803, 33744, 43469, 55251, 69388, 86204, 106050, 129305, 156377, 187704, 223755, 265031, 312066, 365428, 425720, 493581, 569687, 654752, 749529, 854811, 971432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 190. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = A008780(n) - binomial(n, 4) - binomial(n, 3). G.f.: (x^4 - 3*x^3 - 3*x^2 + 5*x + 1)/(x-1)^6. - Colin Barker, Jul 22 2012 a(n) = (n+1)*(n+4)*(n^3 + 40*n^2 + 61*n + 30)/120. - Robert Israel, Jul 06 2016 MAPLE a:= n-> 1+10*n+27*binomial(n, 2)+28*binomial(n, 3)               +11*binomial(n, 4)+binomial(n, 5): seq(a(n), n=0..34); MATHEMATICA LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 11, 48, 140, 326, 657}, 40] (* Harvey P. Dale, Jan 27 2013 *) CoefficientList[Series[(x^4 -3x^3 -3x^2 +5x +1)/(x-1)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 27 2013 *) PROG (MAGMA) [1 + 10*n + 27*Binomial(n, 2) + 28*Binomial(n, 3) + 11*Binomial(n, 4) + Binomial(n, 5): n in [0..40]]; // Vincenzo Librandi, Oct 27 2013 (PARI) my(x='x+O('x^40)); Vec((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6) \\ G. C. Greubel, Feb 17 2019 (Sage) ((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 17 2019 (GAP) List([0..40], n->(n+1)*(n+4)*(n^3+40*n^2+61*n+30)/120); # Muniru A Asiru, Feb 17 2019 CROSSREFS Cf. A007326, A007327, A008780. Sequence in context: A230982 A024530 A117066 * A008780 A211058 A239460 Adjacent sequences:  A042981 A042982 A042983 * A042985 A042986 A042987 KEYWORD nonn,easy AUTHOR Alford Arnold, Aug 15 1998 EXTENSIONS More terms from Erich Friedman STATUS approved

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Last modified June 15 17:11 EDT 2021. Contains 345049 sequences. (Running on oeis4.)