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A075690
a(n) = (n-1)*(n-2)^4 - A028294(n), for n > 4, with a(1) = a(2) = 0, a(3) = 2, and a(4) = 48.
1
0, 0, 2, 48, 304, 999, 2393, 4791, 8542, 14039, 21719, 32063, 45596, 62887, 84549, 111239, 143658, 182551, 228707, 282959, 346184, 419303, 503281, 599127, 707894, 830679, 968623, 1122911, 1294772, 1485479, 1696349, 1928743, 2184066, 2463767
OFFSET
1,3
FORMULA
From G. C. Greubel, Jan 03 2024: (Start)
a(n) = (n-1)*(n-2)^4 - A028294(n) + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].
a(n) = (11*n^4 + 19*n^3 - 632*n^2 + 2012*n - 1686)/6 + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].
G.f.: x^3*(2 + 38*x + 84*x^2 - 61*x^3 - 32*x^4 + 14*x^5 - x^6)/(1-x)^5.
E.g.f.: (1/6)*(-1686 + 1410*x - 498*x^2 + 85*x^3 + 11*x^4)*exp(x) + 281 + 46*x - 23*x^2/2 - 9*x^3/3! + x^4/4!. (End)
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 2, 48, 304, 999, 2393, 4791, 8542}, 50] (* G. C. Greubel, Jan 03 2024 *)
PROG
(Magma) [0, 0, 2, 48] cat [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6: n in [4..50]]; // G. C. Greubel, Jan 03 2024
(SageMath) [0, 0, 2, 48] + [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6 for n in range(4, 51)] # G. C. Greubel, Jan 03 2024
CROSSREFS
Cf. A028294.
Sequence in context: A226401 A226396 A341110 * A101362 A215186 A058090
KEYWORD
nonn
AUTHOR
Jon Perry, Oct 12 2002
EXTENSIONS
More terms from David Wasserman, Jan 22 2005
Name clarified by G. C. Greubel, Jan 03 2024
STATUS
approved