A199043 Expansion of e.g.f. 1/(1+Pi/4-arctan(2*x+1)).

1, 1, 0, -2, 8, -16, -112, 1968, -16896, 55680, 1243392, -32546304, 427932672, -1824506880, -79446663168, 2767039739904, -48592416374784, 243186999164928, 17201692341633024, -744898387504988160, 16285431143888584704, -90779807638034841600

Offset

0,4

Links

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

Formula

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

Mathematica

With[{m = 30}, CoefficientList[Series[1/(1 + Pi/4 - ArcTan[2*x + 1])], {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(m!*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); makelist(a(n), n, 1, 20);
(Sage) m = 30; T = taylor(1/(1+pi/4 -arctan(2*x+1)), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Feb 19 2019

Crossrefs

Sequence in context: A099888 A249308 A353820 * A046161 A092978 A280777

Adjacent sequences: A199040 A199041 A199042 * A199044 A199045 A199046

Keyword

sign

Author

Vladimir Kruchinin, Nov 02 2011

Status

approved