A199042 Expansion of e.g.f. exp(arctan(1+2*x) - Pi/4).

1, 1, -1, -1, 17, -95, 175, 3775, -63775, 533825, 108575, -98151425, 2037293425, -20945772575, -111991234225, 10648024541375, -261756393325375, 3003396413226625, 43283396332525375, -3352997476533082625, 94455063540276700625, -1135469395905648529375

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..425

Formula

a(n) = n! * Sum_{m=1..n} Sum_{k=0..(n-m)/2} (Sum_{i=0..2*k} (2^(i)* stirling1(i+m,m)*C(2*k+m-1,i+m-1))/(i+m)!))*(-1)^(n+m+k)*C(n-1,2*k+m-1) )), n>0; a(0)=1.

Maple

a:=series(exp(arctan(1+2*x)-Pi/4), x=0, 22): seq(n!*coeff(a, x, n), n=0..21); # Paolo P. Lava, Mar 27 2019

Mathematica

With[{m = 30}, CoefficientList[Series[Exp[ArcTan[1+2*x]-Pi/4], {x, 0, m} ], x]*Range[0, m]!] (* G. C. Greubel, Feb 19 2019 *)

Prog

(Maxima) a(n):=if n=0 then 1 else n!*sum(sum((sum((2^(i) *stirling1(i+m, m) *binomial(2*k+m-1, i+m-1))/(i+m)!, i, 0, 2*k))*(-1)^(n+m+k)*binomial(n-1, 2*k+m-1), k, 0, (n-m)/2), m, 1, n);
(Sage) m = 30; T = taylor(exp(arctan(1+2*x)-pi/4)), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Feb 19 2019

Crossrefs

Sequence in context: A213574 A253259 A119783 * A362305 A264211 A094407

Adjacent sequences: A199039 A199040 A199041 * A199043 A199044 A199045

Keyword

sign

Author

Vladimir Kruchinin, Nov 02 2011

Status

approved