A056125 a(n) = (5*n + 4)*binomial(n+7,7)/4.
1, 18, 126, 570, 1980, 5742, 14586, 33462, 70785, 140140, 262548, 469404, 806208, 1337220, 2151180, 3368244, 5148297, 7700814, 11296450, 16280550, 23088780, 32265090, 44482230, 60565050, 81516825, 108548856, 143113608, 186941656
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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GAP
List([0..30], n-> (5*n+4)*Binomial(n+7,7)/4 ); # G. C. Greubel, Jan 19 2020
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Magma
[(5*n+4)*Binomial(n+7,7)/4: n in [0..30]]; // G. C. Greubel, Jan 19 2020
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Maple
seq( (5*n+4)*binomial(n+7,7)/4, n=0..30); # G. C. Greubel, Jan 19 2020
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Mathematica
Table[((5n+4)Binomial[n+7,7])/4,{n,0,30}] (* or *) LinearRecurrence[{9,-36,84, -126,126,-84,36,-9,1},{1,18,126,570,1980,5742,14586,33462,70785},30] (* Harvey P. Dale, Jan 18 2013 *) -
PARI
vector(31, n, (5*n-1)*binomial(n+6,7)/4 ) \\ G. C. Greubel, Jan 19 2020
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Sage
[(5*n+4)*binomial(n+7,7)/4 for n in (0..30)] # G. C. Greubel, Jan 19 2020
Formula
G.f.: (1+9*x)/(1-x)^9.
a(0)=1, a(1)=18, a(2)=126, a(3)=570, a(4)=1980, a(5)=5742, a(6)=14586, a(7)=33462, a(8)=70785, a(n) = 9*a(n-1) -36*a(n-2) +84*a(n-3) -126*a(n-4) + 126*a(n-5) -84*a(n-6) +36*a(n-7) -9*a(n-8) +a(n-9). - Harvey P. Dale, Jan 18 2013
From G. C. Greubel, Jan 19 2020: (Start)
a(n) = 10*binomial(n+8,8) - 9*binomial(n+7,7).
E.g.f.: (20160 + 342720*x + 917280*x^2 + 823200*x^3 + 323400*x^4 + 62328*x^5 + 6076*x^6 + 284*x^7 + 5*x^8)*exp(x)/20160. (End)