A213757 Principal diagonal of the convolution array A213756.
1, 14, 65, 214, 597, 1518, 3649, 8462, 19157, 42646, 93777, 204294, 441781, 949598, 2030849, 4324510, 9174069, 19397574, 40893265, 85981910, 180353621, 377485774, 788527425, 1644165294, 3422550037, 7113537398, 14763947729
Offset: 1
Links
- Clark Kimberling, Table of n, a(n) for n = 1..100
- Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).
Programs
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Mathematica
(See A213756.)
Formula
a(n) = -2 + 2^(n+1) - 6*n + n*2^(n+2) - 3*n^2.
a(n) = 7*a(n-1) - 19*a(n-2) + 25*a(n-3) - 16*a(n-4) + 4*a(n-5).
G.f.: f(x)/g(x), where f(x) = x*(1 + 7*x - 14*x^2) and g(x) = (1 - 2*x)^2 (1 - x)^3.