The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A352638

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Showing entries 1-10 | older changes

Expansion of e.g.f. 1/(1 - 3*sin(x)).
(history; published version)

#17 by Peter Luschny at Sat Mar 26 13:41:09 EDT 2022

STATUS

reviewed

approved

#16 by Michel Marcus at Sat Mar 26 12:53:51 EDT 2022

STATUS

proposed

reviewed

#15 by Vaclav Kotesovec at Sat Mar 26 06:38:11 EDT 2022

STATUS

editing

proposed

#14 by Vaclav Kotesovec at Sat Mar 26 06:37:39 EDT 2022

FORMULA

a(n) ~ n! / (2^(3/2) * arcsin(1/3)^(n+1)). - Vaclav Kotesovec, Mar 26 2022

STATUS

proposed

editing

#13 by Amiram Eldar at Sat Mar 26 05:19:52 EDT 2022

STATUS

editing

proposed

#12 by Amiram Eldar at Sat Mar 26 05:19:50 EDT 2022

MATHEMATICA

With[{m = 17}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*Sin[x]), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)

STATUS

proposed

editing

#11 by Seiichi Manyama at Sat Mar 26 05:16:49 EDT 2022

STATUS

editing

proposed

#10 by Seiichi Manyama at Fri Mar 25 12:33:30 EDT 2022

CROSSREFS

#9 by Seiichi Manyama at Fri Mar 25 12:29:33 EDT 2022

FORMULA

a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * a(n-2*k-1).

#8 by Seiichi Manyama at Fri Mar 25 12:28:39 EDT 2022

PROG

(PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*binomial(n, 2*k+1)*a(n-2*k-1)));