The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065922 Bessel polynomial {y_n}'(4). 6
 0, 1, 27, 846, 32290, 1472535, 78444261, 4789283212, 329976556596, 25336918039005, 2145912573891295, 198763621138900026, 19988975122377164982, 2169175884299414423251, 252661578519463668740745, 31442098485128401965118680, 4163361054820272025075769896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77. LINKS G. C. Greubel, Table of n, a(n) for n = 0..330 FORMULA Recurrence: (n-1)^2*a(n) = (2*n - 1)^3*a(n-1) + n^2*a(n-2). - Vaclav Kotesovec, Jul 22 2015 a(n) ~ 2^(3*n-3/2) * n^(n+1) / exp(n-1/4). - Vaclav Kotesovec, Jul 22 2015 From G. C. Greubel, Aug 14 2017: (Start) a(n) = 2*n*(1/2)_{n}*8^(n - 1)* hypergeometric1f1(1 - n, -2*n, 1/2). E.g.f.: ((1 - 8*x)^(3/2) + 4*x*(1 - 8*x)^(1/2) + 24*x - 1)* exp((1 - sqrt(1 - 8*x))/4)/(16*(1 - 8*x)^(3/2)). (End) G.f.: (t/(1-t)^3)*hypergeometric2f0(2,3/2; - ; 8*t/(1-t)^2). - G. C. Greubel, Aug 16 2017 MATHEMATICA Table[Sum[(n+k+1)!*2^(k-1)/((n-k-1)!*k!), {k, 0, n-1}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 22 2015 *) RecurrenceTable[{a[0]==0, a[1]==1, a[n]==((2n-1)^3 a[n-1]+n^2 a[n-2])/ (n-1)^2}, a, {n, 20}] (* Harvey P. Dale, May 23 2016 *) PROG (PARI) for(n=0, 50, print1(sum(k=0, n-1, (n+k+1)!*2^(k-1)/((n-k-1)!*k!)), ", ")) \\ G. C. Greubel, Aug 14 2017 CROSSREFS Cf. A001514, A065920, A065921. Sequence in context: A218717 A159234 A120715 * A061695 A107050 A129999 Adjacent sequences:  A065919 A065920 A065921 * A065923 A065924 A065925 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 08 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)