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A012150 exp(tan(arcsin(x))) = 1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+76/5!*x^5... 1
1, 1, 1, 4, 13, 76, 421, 3256, 25369, 245008, 2449801, 28441216, 346065061, 4700478784, 67243537453, 1047088053376, 17192488230961, 302112622479616, 5593309059948049, 109527844826856448, 2255588021494237501 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..20.

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582

FORMULA

From Vladimir Kruchinin, Feb 17 2011: (Start)

a(n) = n!*sum_{k=1..n} A111959(n-1,k-1)*2^(k-n)/k!.

a(n) = n!*sum_{k=1..n} (1+(-1)^(n-k))*C((n-2)/2,(n-k)/2)/(2*k!), n>0.

E.g.f.: exp(x/sqrt(1-x^2)). (End)

E.g.f.: S(x) = exp(x/sqrt(1-x^2)) = 1 + 2*(x/sqrt(1-x^2))/(G(0) - x/sqrt(1-x^2)), G(k) = 8*k + 2 + (x^2)/((1-x^2)*(8*k+6) + x^2/G(k+1)); (continued fraction). - Sergei N. Gladkovskii, Dec 16 2011

a(n) = (3*n^2 - 12*n + 13)*a(n-2) - 3*(n-4)*(n-3)^2*(n-2)*a(n-4) + (n-6)*(n-5)*(n-4)^2*(n-3)*(n-2)*a(n-6). - Vaclav Kotesovec, Nov 08 2013

a(n) ~ n^(n-1/3) * exp(3/2*n^(1/3)-n) / sqrt(3) * (1 - 19/(36*n^(1/3)) + 553/(2592*n^(2/3))). - Vaclav Kotesovec, Nov 08 2013

MAPLE

A012150 := proc(n) if n = 0 then 1; else add( (1+(-1)^(n-k)) *binomial((n-2)/2, (n-k)/2)/(2*k!), k=1..n) ; %*n! ; end if; end proc: # R. J. Mathar, Mar 20 2011

MATHEMATICA

Range[0, 20]! CoefficientList[Series[Exp[Tan[ArcSin[x]]], {x, 0, 20}], x] (* Or *)

f[n_] := n! Sum[(1 + (-1)^(n - k)) Binomial[(n - 2)/2, (n - k)/2]/2/k!, {k, n}]; f[0] = 1; Array[f, 21, 0] (* Robert G. Wilson v, Feb 19 2011 *)

CROSSREFS

Sequence in context: A171756 A235385 A144055 * A012261 A012075 A197942

Adjacent sequences:  A012147 A012148 A012149 * A012151 A012152 A012153

KEYWORD

nonn

AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)

STATUS

approved

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Last modified September 16 08:36 EDT 2019. Contains 327091 sequences. (Running on oeis4.)