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A290071
a(n) = (1/48)*n*(n+5)^2*(1*n^3 + 7*n^2 + 16*n + 28).
3
0, 39, 196, 664, 1809, 4250, 8954, 17346, 31434, 53949, 88500, 139744, 213571, 317304, 459914, 652250, 907284, 1240371, 1669524, 2215704, 2903125, 3759574, 4816746, 6110594, 7681694, 9575625, 11843364, 14541696, 17733639, 21488884, 25884250, 31004154, 36941096
OFFSET
0,2
FORMULA
From Colin Barker, Jul 20 2017: (Start)
G.f.: x*(39 - 77*x + 111*x^2 - 88*x^3 + 36*x^4 - 6*x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6.
(End)
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 39, 196, 664, 1809, 4250, 8954}, 40] (* Harvey P. Dale, Nov 15 2022 *)
PROG
(PARI) concat(0, Vec(x*(39 - 77*x + 111*x^2 - 88*x^3 + 36*x^4 - 6*x^5) / (1 - x)^7 + O(x^50))) \\ Colin Barker, Jul 20 2017
(PARI) vector(50, n, n*(n+5)^2*(n^3+7*n^2+16*n+28)/48) \\ Derek Orr, Jul 24 2017
CROSSREFS
This is the negation of column 4 in triangle A290053.
Sequence in context: A193228 A243578 A124619 * A221797 A068975 A177709
KEYWORD
nonn,easy
AUTHOR
STATUS
approved