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A370669
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Expansion of Sum_{k>=0} k! * ( x/(1+x^2) )^k.
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1
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1, 1, 2, 5, 20, 103, 630, 4475, 36232, 329341, 3320890, 36787889, 444125628, 5803850515, 81625106990, 1229298774647, 19738870726160, 336627732586105, 6076590994501938, 115752541255203869, 2320456607696181220, 48833227436258924671, 1076420625931284514342
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-2*k)! * binomial(n-k-1,k).
a(n) = n*a(n-1) + (n-4)*a(n-3) + a(n-4) for n > 4.
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x/(1+x^2))^k))
(PARI) a(n) = sum(k=0, n\2, (-1)^k*(n-2*k)!*binomial(n-k-1, k));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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