A189780 E.g.f.: 1/(1-arcsin(x)).

1, 1, 2, 7, 32, 189, 1328, 11019, 104064, 1111641, 13166592, 172006671, 2448559104, 37814647701, 628513744896, 11201565483219, 212867324706816, 4299987047933745

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

a(n) ~ cos(1) * n! / (sin(1))^(n+1). - Vaclav Kotesovec, Nov 06 2014

Mathematica

CoefficientList[Series[1/(1-ArcSin[t]), {t, 0, 100}], t] Table[
n!, {n, 0, 100}] (* Emanuele Munarini, Nov 23 2015 *)

Prog

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

Crossrefs

Sequence in context: A352435 A000987 A006957 * A195983 A079265 A270229

Adjacent sequences: A189777 A189778 A189779 * A189781 A189782 A189783

Keyword

nonn

Author

Vladimir Kruchinin, May 02 2011

Status

approved