A281588 - OEIS

A281588

E.g.f. z*(2*(exp(z) + 1)/(cosh(z) + cos(z)) - 1).

0, 1, 2, 3, 4, -5, -24, -98, -272, 621, 4960, 31856, 132672, -437593, -4893056, -42854160, -237969664, 1026405753, 14756156928, 163699919104, 1136284574720, -6054175060941, -106379840985088, -1428593836836352, -11899498670002176, 75477454065058725

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

L. Seidel, Über eine einfache Entstehungsweise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, Vol. 7 (1877), 157-187.

MAPLE

A281588_list := proc(n) z*(2*(exp(z)+1)/(cosh(z)+cos(z))-1);

series(%, z, n+1); seq(k!*coeff(%, z, k), k=0..n) end: A281588_list(25);

PROG

(Sage)

def SIB(dim, m): # Algorithm of L. Seidel (1877).

E = matrix(ZZ, dim)

def plow(n, dir):

if dir : # right to left backward

E[n, 0] = int(n == 1)

for k in range(n-1, -1, -1) :

E[k, n-k] = E[k+1, n-k-1] - E[k, n-k-1]

else: # left to right forward

E[0, n] = 0

for k in range(1, n+1, 1) :

E[k, n-k] = E[k-1, n-k+1] + E[k-1, n-k]

dir = [mod(n, m) == 1 for n in (0..dim-1)]

for n in (0..dim-1): plow(n, dir[n])

return [E[0, k] if dir[k] else E[k, 0] for k in range(dim)]

A281588_list = lambda len: SIB(len, 4)

A281588_list(26)

CROSSREFS

Cf. A281587.

Sequence in context: A239448 A248713 A242799 * A088865 A237342 A075807

Adjacent sequences: A281585 A281586 A281587 * A281589 A281590 A281591

KEYWORD

sign

AUTHOR

Peter Luschny, Feb 01 2017

STATUS

approved