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A012123
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exp(arcsin(tanh(x)))=1+x+1/2!*x^2-3/4!*x^4-4/5!*x^5+21/6!*x^6...
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3
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1, 1, 1, 0, -3, -4, 21, 80, -263, -2224, 4841, 88960, -99723, -4942144, -199939, 366928640, 501445617, -35219691264, -101818966319, 4251941253120, 19731909099757, -631113275843584, -4192563651606299
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| a(n) = (-I)^n * Z(n,I), where I = sqrt(-1) and Z(n,x) denotes the n-th zigzag polynomial as described in A147309. Alternative form of the egf: {sec(I*x) -tan(I*x)}^I. - Peter Bala, Jan 26 2011
a(n)=sum(m=1..n, sum(r=m..n, (sum(k=r..n, (-1)^((3*k)/2)*(sum(i=0..k, (2^i*stirling1(m+i,m)* binomial(m+k-1,m+i-1))/(m+i)!))*binomial((r-2)/2,(r-m-k)/2)))*((-1)^(r-m)+1)*sum(k=0..r-m, binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k))))/2, n>0, a(0)=1. [From Vladimir Kruchinin, Jun 09 2011]
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PROG
| (Maxima)
a(n):=sum(sum((sum((-1)^((3*k)/2)*(sum((2^i*stirling1(m+i, m)* binomial(m+k-1, m+i-1))/(m+i)!, i, 0, k))*binomial((r-2)/2, (r-m-k)/2), k, 0, r-m))*((-1)^(r-m)+1)*sum(binomial(k-1, r-1)*k!*2^(n-k)*stirling2(n, k)*(-1)^(r+k), k, r, n), r, m, n), m, 1, n)/2; [From Vladimir Kruchinin, Jun 09 2011]
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CROSSREFS
| Sequence in context: A156173 A094632 A081698 * A012255 A012247 A057791
Adjacent sequences: A012120 A012121 A012122 * A012124 A012125 A012126
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KEYWORD
| sign
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AUTHOR
| Patrick Demichel (dml(AT)hpfrcu03.france.hp.com)
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