A281588 -id:A281588 - cp's OEIS frontend

A281587 Triangle read by rows, e.g.f. exp(xz)(2*(exp(z)+1)/(cosh(z)+cos(z))-1).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, -1, 4, 6, 4, 1, -4, -5, 10, 10, 5, 1, -14, -24, -15, 20, 15, 6, 1, -34, -98, -84, -35, 35, 21, 7, 1, 69, -272, -392, -224, -70, 56, 28, 8, 1, 496, 621, -1224, -1176, -504, -126, 84, 36, 9, 1, 2896, 4960, 3105, -4080, -2940, -1008, -210, 120, 45, 10, 1

Offset: 0

Peter Luschny, Feb 01 2017

			Triangle starts:
[   1]
[   1,   1]
[   1,   2,   1]
[   1,   3,   3,   1]
[  -1,   4,   6,   4,  1]
[  -4,  -5,  10,  10,  5,  1]
[ -14, -24, -15,  20, 15,  6, 1]
[ -34, -98, -84, -35, 35, 21, 7, 1]

Cf. A130595 (m=1), A109449 (m=2), A215064 (m=3), A281587 (m=4).

Cf. A178964 (col. 0), A281588 (col. 1).

A281587_row := proc(n) exp(x*z)*(2*(exp(z)+1)/(cosh(z)+cos(z))-1);
n!*coeff(series(%,z,n+1),z,n); PolynomialTools:-CoefficientList(%,x) end:
for n from 0 to 12 do A281587_row(n) od;

A281586 E.g.f.: z(((exp(z)+1)/((exp(z)+2exp(-z/2)cos(zsqrt(3)/2))/3))-1).

Original entry on oeis.org

0, 1, 2, 3, -4, -15, -54, 133, 792, 4293, -15130, -123849, -895212, 4101799, 42732522, 386103915, -2177360656, -27544520691, -298649804706, 1999963458217, 29765143177020, 376514568163377, -2919514870785766, -49968285360277437, -722370834074695896, 6365117686550339275

Offset: 0

Peter Luschny, Jan 25 2017

sign

a(n) = A215064(n,1).

A281586_list := proc(len) z*(((exp(z)+1)/((exp(z)+2*exp(-z/2)* cos(z*sqrt(3)/2))/3))-1); series(%,z,len+1); seq(k!*coeff(%,z,k),k=0..len) end: A281586_list(20);

# uses[SIB from A281588]
A281586_list = lambda len: SIB(len, 3)
print(A281586_list(26))

cp's OEIS Frontend

A281587 Triangle read by rows, e.g.f. exp(xz)(2*(exp(z)+1)/(cosh(z)+cos(z))-1).

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Maple

A281586 E.g.f.: z(((exp(z)+1)/((exp(z)+2exp(-z/2)cos(zsqrt(3)/2))/3))-1).

Views

Author

Keywords

Crossrefs

Programs

Maple

Sage

cp's OEIS Frontend

A281587 Triangle read by rows, e.g.f. exp(x*z)*(2*(exp(z)+1)/(cosh(z)+cos(z))-1).

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

A281586 E.g.f.: z*(((exp(z)+1)/((exp(z)+2*exp(-z/2)*cos(z*sqrt(3)/2))/3))-1).

Views

Author

Keywords

Crossrefs

Programs

Maple

Sage

A281587 Triangle read by rows, e.g.f. exp(xz)(2*(exp(z)+1)/(cosh(z)+cos(z))-1).

A281586 E.g.f.: z(((exp(z)+1)/((exp(z)+2exp(-z/2)cos(zsqrt(3)/2))/3))-1).