A357711 Expansion of e.g.f. cosh( 2 * log(1-x) ).
1, 0, 4, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800, 3113510400, 43589145600, 653837184000, 10461394944000, 177843714048000, 3201186852864000, 60822550204416000, 1216451004088320000, 25545471085854720000, 562000363888803840000
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Pochhammer Symbol.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(cosh(2*log(1-x)))) -
PARI
a(n) = sum(k=0, n\2, 4^k*abs(stirling(n, 2*k, 1)));
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PARI
a(n) = (prod(k=0, n-1, 2+k)+prod(k=0, n-1, -2+k))/2;
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=2, n, v[i+1]=(2*i-3)*v[i]-(i^2-4*i)*v[i-1]); v;
Formula
a(n) = Sum_{k=0..floor(n/2)} 4^k * |Stirling1(n,2*k)|.
a(n) = ( (2)_n + (-2)_n )/2, where (x)_n is the Pochhammer symbol.
a(n) = (n+1)!/2 for n > 2.
a(0) = 1, a(1) = 0; a(n) = (2*n-3) * a(n-1) - (n^2-4*n) * a(n-2).