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A317982
Expansion of 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.
5
406, 13818, 115836, 545860, 1858290, 5124126, 12182968, 25945416, 50745870, 92745730, 160386996, 264896268, 420839146, 646725030, 965662320, 1406064016, 2002403718, 2796022026, 3835983340, 5179983060, 6895305186, 9059830318, 11763094056, 15107395800
OFFSET
1,1
COMMENTS
Seems to be the second column of A316387.
FORMULA
G.f.: 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.
a(n) = 70*n^6 + 210*n^5 + 175*n^4 - 42*n^2 - 7*n.
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>7.
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {406, 13818, 115836, 545860, 1858290, 5124126, 12182968}, 30] (* Harvey P. Dale, Nov 15 2022 *)
PROG
(PARI) Vec(14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7 + O(x^40))
(PARI) a(n) = 70*n^6 + 210*n^5 + 175*n^4 - 42*n^2 - 7*n
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Aug 13 2018
STATUS
approved