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A012136 Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only). 0
1, 5, 129, 7797, 848481, 145041093, 35799178401, 12045448529397, 5298881528389185, 2952169020073027845, 2031522244065649876545, 1692164698229362361298165, 1677876856826199251515980705 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..13.

FORMULA

a(n) = (2*n+1)!*sum(k=0..n, 16^(-k)*binomial(2*k,k)*(2*k+1)!*sum(i=2*k+1..2*n+1, (2^i*Stirling1(i,2*k+1)*binomial(2*n,i-1))/i!))/2. - Vladimir Kruchinin, Jun 17 2011

EXAMPLE

tan(arcsin(arctanh(x))) = x + (5/3!)*x^3 + (129/5)!*x^5 + (7797/7!)*x^7 + (848481/9!)*x^9 + ...

PROG

(Maxima)

a(n):=(2*n+1)!*sum(16^(-k)*binomial(2*k, k)*(2*k+1)!*sum((2^i*stirling1(i, 2*k+1)*binomial(2*n, i-1))/i!, i, 2*k+1, 2*n+1), k, 0, n)/2; /* Vladimir Kruchinin, Jun 17 2011 */

CROSSREFS

Sequence in context: A230303 A094074 A012218 * A012022 A012176 A012187

Adjacent sequences: A012133 A012134 A012135 * A012137 A012138 A012139

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified December 1 16:09 EST 2022. Contains 358468 sequences. (Running on oeis4.)