0,2

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.

Harry J. Smith, Table of n, a(n) for n=0,...,100

Index entries for sequences related to Bessel functions or polynomials

y_n(x) = sum ((n+k)!*(x/2)^k/((n-k)!*k!), k=0..n);

Main diagonal of A143411. Recurrence relation: a(0) = 1, a(1) = 5, a(n) = 4*(2*n-1)*a(n-1) + a(n-2) for n >= 2. Sequence A143412(n) satisfies the same recurrence relation. 1/sqrt(e) = 1 - 2*sum {n = 0..inf} (-1)^n/(a(n)*a(n+1)) = 1 - 2*(1/(1*5) - 1/(5*61) + 1/(61*1225) - ...). [From Peter Bala (pbala(AT)toucansurf.com), Aug 14 2008]

(PARI) { for (n=0, 100, if (n>1, a=4*(2*n - 1)*a1 + a2; a2=a1; a1=a, if (n, a=a1=5, a=a2=1)); write("b065919.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 04 2009]

Cf. A001515, A001517, A001518.

Polynomial coefficients are in A001498.

A143411 (main diagonal), A143412. [From Peter Bala (pbala(AT)toucansurf.com), Aug 14 2008]

Sequence in context: A146760 A083082 A009825 this_sequence A096537 A115047 A028296

Adjacent sequences: A065916 A065917 A065918 this_sequence A065920 A065921 A065922

nonn

N. J. A. Sloane (njas(AT)research.att.com), Dec 08 2001

Recurrence relation a(2) = 5 corrected to a(1) = 5 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 04 2009