A381374 Little Hankel transform of A317614: a(n) = A317614(n+1)^2 - A317614(n)*A317614(n+2).
1, 1, 97, 49, 769, 289, 2977, 961, 8161, 2401, 18241, 5041, 35617, 9409, 63169, 16129, 104257, 25921, 162721, 39601, 242881, 58081, 349537, 82369, 487969, 113569, 663937, 152881, 883681, 201601, 1153921, 261121, 1481857, 332929, 1875169, 418609, 2342017, 519841, 2891041
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (0,5,0,-10,0,10,0,-5,0,1).
Programs
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Mathematica
LinearRecurrence[{0,5,0,-10,0,10,0,-5,0,1},{1,97,49,769,289,2977,961,8161,2401,18241},38]
Formula
a(n) = (10 + 6*(-1)^n + 4*n*(n + 2)*(3*(n + 1)^2 + (-1)^n*(2*n^2 + 4*n + 5)))/16.
a(n) = 5*a(n-2) - 10*a(n-4) + 10*a(n-6) - 5*a(n-8) + a(n-10) for n > 10.
G.f.: (1 + x + 92*x^2 + 44*x^3 + 294*x^4 + 54*x^5 + 92*x^6 - 4*x^7 + x^8 + x^9)/(1 - x^2)^5.
E.g.f.: ((4 + 3*x + 123*x^2 + 10*x^3 + 5*x^4)*cosh(x) + (1 + 69*x + 21*x^2 + 50*x^3 + x^4)*sinh(x))/4.
a(2*n) = A239607(n).