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A357711 Expansion of e.g.f. cosh( 2 * log(1-x) ). 2
1, 0, 4, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800, 3113510400, 43589145600, 653837184000, 10461394944000, 177843714048000, 3201186852864000, 60822550204416000, 1216451004088320000, 25545471085854720000, 562000363888803840000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Pochhammer Symbol.
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).
PROG
(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)));
(PARI) a(n) = (prod(k=0, n-1, 2+k)+prod(k=0, n-1, -2+k))/2;
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; v[2]=0; for(i=2, n, v[i+1]=(2*i-3)*v[i]-(i^2-4*i)*v[i-1]); v;
CROSSREFS
Column k=4 of A357712.
Cf. A065143.
Sequence in context: A335656 A355268 A286073 * A337291 A324693 A276707
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 10 2022
STATUS
approved

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Last modified June 19 19:59 EDT 2024. Contains 373507 sequences. (Running on oeis4.)