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URL: https://oeis.org/A231622

⇱ A231622 - OEIS

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A231622
(2*n+1)*a(n+1) = (4*n^2+1)*a(n) + (2*n+1)*a(n-1) with n>1, a(0)=2, a(1)=-1.
2
2, -1, 1, 4, 31, 293, 3326, 44189, 673471, 11588884, 222304897, 4704612119, 108897613826, 2737023412199, 74236203425281, 2161288643251828, 67228358271588991, 2225173863019549229, 78087247031912850686, 2896042595237791161749, 113184512236563589997407
OFFSET
0,1
LINKS
FORMULA
E.g.f. A(x) satisfies 0 = f(A(x), A'(x), A''(x)) where f(u0, u1, u2) = (3 + 2*x)*u0 + (5 + 2*x)*u1 + (-1 + 4*x^2)*u2.
a(-n) = a(n). a(n) = A003436(n) if n>1.
a(n) = (-1)^n*2*hypergeom([n, -n], [], 1/2). - Peter Luschny, Nov 10 2016
EXAMPLE
G.f. = 2 - x + x^2 + 4*x^3 + 31*x^4 + 293*x^5 + 3326*x^6 + 44189*x^7 + ...
MAPLE
A231622 := n -> (-1)^n*2*hypergeom([n, -n], [], 1/2):
seq(simplify(A231622(n)), n=0..19); # Peter Luschny, Nov 10 2016
MATHEMATICA
a[ n_] := With[{m = Abs@n}, Boole[m == 0] + (2*m - 1)!! Hypergeometric1F1[ -m, 1 - 2*m, -2]]
PROG
(PARI) {a(n) = n=abs(n); if( n<2, 2 - 3*(n>0), ( a(n-1) * (4*n^2 - 8*n + 5) + a(n-2) * (2*n-1) ) / (2*n-3))}
CROSSREFS
Cf. A003436.
Sequence in context: A326570 A184880 A257859 * A165623 A374358 A264878
KEYWORD
sign
AUTHOR
Michael Somos, Nov 11 2013
STATUS
approved