A065951 Bessel polynomial {y_n}'''(-1).
0, 0, 0, 90, -1890, 36540, -729540, 15507450, -353908170, 8680615020, -228436914420, 6431738433120, -193144902350400, 6166945337372820, -208728050864680620, 7467661073819689470, -281666767117960443870, 11173071188540083124700
Offset: 0
Keywords
References
- J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
Links
Programs
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Mathematica
Join[{0, 0, 0}, Table[48*Binomial[n, 3]*Pochhammer[1/2, n]*(-2)^(n - 3)* Hypergeometric1F1[3 - n, -2*n, -2], {n,3,50}]] (* G. C. Greubel, Aug 15 2017 *) CoefficientList[Series[(90*t^3/(1 - t)^7)*HypergeometricPFQ[{4, 7/2}, {}, -2*t/(1 - t)^2], {t, 0, 50}], t] (* G. C. Greubel, Aug 16 2017 *) -
PARI
for(n=0,50, print1(sum(k=0,n-3, ((n+k+3)!/(8*(n-k-3)!*k!))*(-2)^k ), ", ")) \\ G. C. Greubel, Aug 15 2017
Formula
a(n) = 48*binomial(n,3)*(1/2){n}*(-2)^(n - 3)*hypergeometric1f1(3-n, -2*n, -2), where (a){n} is the Pochhammer symbol. - G. C. Greubel, Aug 15 2017
G.f.: (90*x^3/(1-x)^7)*hypergeometric2f0(4,7/2; - ; -2*x/(1-x)^2). - G. C. Greubel, Aug 16 2017
D-finite with recurrence (-n+3)*a(n) +(-2*n^2+11)*a(n-1) +(-2*n^2+8*n+3)*a(n-2) +(n+1)*a(n-3)=0. - R. J. Mathar, Jul 25 2022