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A156926 Row sums of the FP2 polynomials of A156925. 1
1, 2, -8, -96, 4608, 1105920, -1592524800, -16052649984000, 1294485694709760000, 939485937792555417600000, -6818413142123250198773760000000, -544338467423010707068824846336000000000, 521477993674340011006196823029396275200000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

|a(n)| is the 2^n times the determinant of the n X n matrix whose element (i,j) equals i^j. - Michel Lagneau, Feb 08 2021

LINKS

Table of n, a(n) for n=0..12.

FORMULA

Row sum(n+1) = (-1)^(n)*2*(n+1)!*Row sum(n) with Row sum(n=0) = 1.

Let A(x)=sum(k>=0, |a(k)|*x^k  ), then A(x)= G(0)/2, where G(k)= 1  + 1/(1 - 2*x*(k+1)!/(2*x*(k+1)! + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 10 2013

Let A(x)=sum(k>=0, |a(k)|*x^k  ), then A(x)= G(0)/(4*x)- 1/(2*x), where G(k)= 1  + 1/(1 - 2*x*(2*k)!/(2*x*(2*k)! + 1/(1  + 1/(1 - 2*x*(2*k+1)!/(2*x*(2*k+1)! + 1/G(k+1) ))))); (continued fraction). - Sergei N. Gladkovskii, Jul 10 2013

a(n) = A000079(n) * A000178(n) * A057077(n). - Alois P. Heinz, Feb 09 2021

MAPLE

a:= proc(n) option remember;

      `if`(n=0, 1, -2*n!*a(n-1)*(-1)^n)

    end:

seq(a(n), n=0..14);  # Alois P. Heinz, Feb 09 2021

PROG

(PARI) for(n=0, 12, print1((-1)^(n\2)*2^n*matdet(matrix(n, n, i, j, i^j)), ", ")) \\ Hugo Pfoertner, Feb 09 2021

CROSSREFS

Row sums of A156925.

Cf. A000079, A000178, A057077.

Sequence in context: A322736 A137704 A001417 * A326866 A001697 A006069

Adjacent sequences:  A156923 A156924 A156925 * A156927 A156928 A156929

KEYWORD

easy,sign

AUTHOR

Johannes W. Meijer, Feb 20 2009

STATUS

approved

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Last modified May 15 08:59 EDT 2021. Contains 343909 sequences. (Running on oeis4.)