A078634 E.g.f. exp( 1 - x - sqrt( 1 - 4*x + x^2 )).

1, 1, 4, 28, 289, 3991, 69391, 1458199, 35976298, 1019869624, 32674379941, 1167655730341, 46053354678409, 1987219627288273, 93128105830564624, 4710372032469481876, 255762372971187607501, 14838749685456807409159

Offset

0,3

Comments

Moments of a probability density function.

Links

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

Formula

E.g.f.: exp( 1 - x - sqrt( 1 - 4*x + x^2 )).

a(n) ~ sqrt(2*sqrt(3)-3)*exp(sqrt(3)-n-1)*n^(n-1)*(2+sqrt(3))^n. - Vaclav Kotesovec, Sep 29 2013

D-finite with recurrence: a(n) +(-4*n+9)*a(n-1) +(n^2-16*n+26)*a(n-2) +(3*n^2-23*n+39)*a(n-3) +2*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jan 25 2020

Mathematica

Table[n!, {n, 0, 17}]* CoefficientList[ Series[ Exp[1 - x - Sqrt[1 - 4x + x^2]], {x, 0, 17}], x]

Prog

(PARI) {a(n)=if(n<0, 0, n!*polcoeff( exp(1-x-sqrt(1-4*x+x^2+x*O(x^n))), n))} /* Michael Somos, Sep 20 2006 */

Crossrefs

Sequence in context: A360832 A201595 A076729 * A091485 A201354 A112938

Adjacent sequences: A078631 A078632 A078633 * A078635 A078636 A078637

Keyword

nonn,easy

Author

Scott Peters (speters(AT)pinnaclesys.com), Dec 12 2002

Extensions

Edited and extended by Robert G. Wilson v and Benoit Cloitre, Dec 13 2002

Status

approved