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A114211
a(n) = (5*n^3+12*n^2+n+6)/6.
0
1, 4, 16, 42, 87, 156, 254, 386, 557, 772, 1036, 1354, 1731, 2172, 2682, 3266, 3929, 4676, 5512, 6442, 7471, 8604, 9846, 11202, 12677, 14276, 16004, 17866, 19867, 22012, 24306, 26754, 29361, 32132, 35072, 38186, 41479
OFFSET
0,2
COMMENTS
Column 3 of A114202. Third differences are 1,1,7,5,5,5,5,5,... with g.f. (1+6x^2-2x^3)/(1-x).
FORMULA
G.f.: (1+6*x^2-2*x^3)/(1-x)^4 = (1+3*(x/(1-x))+9*(x/(1-x))^2+5*(x/(1-x))^3)/(1-x).
a(n) = sum{k=0..n, C(n, k)*C(3, k)*J(k+1)} where J(n)=A001045(n).
a(0)=1, a(n)=a(n-1)+(n-1)*(n+2)+A104249(n).
EXAMPLE
[1,3,9,5]=[1*1,3*1,3*3,1*5]=[C(3,0)*J(1),C(3,1)*J(2),C(3,2)*J(3),C(3,3)*J(4)].
MATHEMATICA
CoefficientList[Series[(1+6x^2-2x^3)/(1-x)^4, {x, 0, 75}], x] (* Harvey P. Dale, Mar 06 2011 *)
CROSSREFS
Sequence in context: A056373 A018828 A323847 * A188124 A344857 A190090
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 17 2005
STATUS
approved