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A113871 G.f.: 1/(Sum_{k>=0} (k!)^2 x^k). 6
1, -1, -3, -29, -499, -13101, -486131, -24266797, -1571357619, -128264296301, -12894743113075, -1566235727656365, -226180775756251955, -38308065207361046509, -7521255169156107737331, -1694604321825062440852013, -434302821056087233474158259 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Marcelo Aguiar and Swapneel Mahajan, On The Hadamard product Of Hopf monoids
John D. Dixon, Asymptotics of Generating the Symmetric and Alternating Groups, Electronic Journal of Combinatorics, 2005, vol 11(2), R56.
FORMULA
G.f.: 2/Q(0), where Q(k) = 1 + 1/(1 - (k+1)^2*x/((k+1)^2*x + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 17 2013
a(n) ~ -n!^2 * (1 - 2/n^2 - 5/n^4 - 10/n^5 - 67/n^6 - 332/n^7 - 2152/n^8 - 14946/n^9 - 115583/n^10). - Vaclav Kotesovec, Jul 28 2015
a(0) = 1, a(n) = -Sum_{k=0..n-1} a(k) * ((n-k)!)^2. - Daniel Suteu, Feb 23 2018
MATHEMATICA
nn = 20; CoefficientList[Series[1/Sum[(k!)^2 x^k, {k, 0, nn}], {x, 0, nn}], x] (* T. D. Noe, Jan 03 2013 *)
PROG
(Sage)
h = 1/(1+x*hypergeometric((1, 2, 2), (), x))
taylor(h, x, 0, 16).list() # Peter Luschny, Jul 28 2015
(Sage)
def A113871_list(len):
R, C = [1], [1]+[0]*(len-1)
for n in (1..len-1):
for k in range(n, -1, -1):
C[k] = C[k-1] * k^2
C[0] = -sum(C[k] for k in (1..n))
R.append(C[0])
return R
print(A113871_list(17)) # Peter Luschny, Jul 30 2015
CROSSREFS
Sequence in context: A370922 A366005 A326433 * A186451 A248828 A210827
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Jan 26 2006
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)