A191500 E.g.f. sqrt(1+arctan(2*x))

1, 1, -1, -5, 17, 249, -1489, -27453, 237537, 6037041, -68649441, -2107439157, 29789919345, 1092524775081, -18492402857265, -781266357571053, 15425010795541185, 739391174869277025, -16695627953904545985, -893468264544135234405, 22725280358984904476625

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n)=2*n!*sum(k=0..(n-1)/2, ((-1)^(n+k+1)*binomial(2*n-4*k-2,n-2*k-1)*(n-2*k-1)!*(sum(i=0..2*k, (2^(i+4*k-n)*stirling1(i+n-2*k,n-2*k)*binomial(n-1,i+n-2*k-1))/(i+n-2*k)!)))), n>0, a(0)=1.

Mathematica

With[{nn=20}, CoefficientList[Series[Sqrt[1+ArcTan[2x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 20 2021 *)

Prog

(Maxima)
a(n):=2*n!*sum(((-1)^(n+k+1)*binomial(2*n-4*k-2, n-2*k-1)*(n-2*k-1)!*(sum((2^(i+4*k-n)*stirling1(i+n-2*k, n-2*k)*binomial(n-1, i+n-2*k-1))/(i+n-2*k)!, i, 0, 2*k))), k, 0, (n-1)/2);

Crossrefs

Sequence in context: A086362 A195570 A281504 * A089894 A077718 A235461

Adjacent sequences: A191497 A191498 A191499 * A191501 A191502 A191503

Keyword

sign

Author

Vladimir Kruchinin, Jun 03 2011

Status

approved