A093615 E.g.f. equals the ratio of two power series, each with triangular exponents of x.

0, 1, -1, 3, -15, 85, -570, 4509, -40804, 414864, -4686570, 58245650, -789691134, 11598605460, -183459343613, 3109122970590, -56203651969935, 1079493501290439, -21953265755518782, 471258656426134701, -10648683969964745520, 252651472831081785300

Offset

0,4

Comments

E.g.f. is asymptotic to 1-1/(2x). Compare to e.g.f. of A093523.

Links

Robert Israel, Table of n, a(n) for n = 0..440

Formula

E.g.f: T1(x)/T0(x), where T0(x) = sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)! and T1(x) = sum_{n>=0} x^(n*(n+1)/2+1)/(n*(n+1)/2+1)!; T0(r)=0 at r=-0.8851021553904208809237177147294641529670...

Maple

N:= 10: # to get a(0)..a((N+1)*(N+2)/2-1)
T0:= add(x^(n*(n+1)/2)/(n*(n+1)/2)!, n=0..N):
T1:= add(x^(1+n*(n+1)/2)/(1+n*(n+1)/2)!, n=0..N):
S:= series(T1/T0, x, (N+1)*(N+2)/2):
seq(coeff(S, x, n)*n!, n=0..(N+1)*(N+2)/2-1); # Robert Israel, Jan 01 2018

Prog

(PARI) T0(x)=sum(k=0, sqrtint(2*n)+1, x^(k*(k+1)/2)/(k*(k+1)/2)!)
(PARI) T1(x)=sum(k=0, sqrtint(2*n)+1, x^(k*(k+1)/2+1)/(k*(k+1)/2+1)!)
(PARI) a(n)=n!*polcoeff(T1(x)/T0(x)+x*O(x^n), n)

Crossrefs

Cf. A093523.

Sequence in context: A182016 A127085 A326275 * A191148 A001931 A306524

Adjacent sequences: A093612 A093613 A093614 * A093616 A093617 A093618

Keyword

sign

Author

Paul D. Hanna, Apr 05 2004

Status

approved