A113871 G.f.: 1/(Sum_{k>=0} (k!)^2 x^k).

1, -1, -3, -29, -499, -13101, -486131, -24266797, -1571357619, -128264296301, -12894743113075, -1566235727656365, -226180775756251955, -38308065207361046509, -7521255169156107737331, -1694604321825062440852013, -434302821056087233474158259

Offset

0,3

Links

T. D. Noe, Table of n, a(n) for n = 0..100

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

Cf. A003319, A051296, A113869, A114038, A316862.

Sequence in context: A366005 A376038 A326433 * A377832 A186451 A248828

Adjacent sequences: A113868 A113869 A113870 * A113872 A113873 A113874

Keyword

sign

Author

N. J. A. Sloane, Jan 26 2006

Status

approved