A089518 Third column (k=5) of array A078741 ((3,3)-Stirling2) divided by 9.

1, 138, 10476, 683208, 42315696, 2570768928, 155010407616, 9318969502848, 559578466388736, 33585275183251968, 2015370124337581056, 120928294183739148288, 7255843732407562776576, 435354129897768445943808

Offset: 0

Author

Wolfdieter Lang, Dec 01 2003

Keywords

• nonn
• easy

References

• P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

Links

• P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.
• Index entries for linear recurrences with constant coefficients, signature (90, -1944, 8640).

Crossrefs

Cf. A089513 (third column of A089504), A089519, A090219.

Formula

G.f.: (1+48*x)/((1-3*2*1*x)*(1-4*3*2*x)*(1-5*4*3*x)).

a(n)= (10*(5*4*3)^n - 8*(4*3*2)^n + (3*2*1)^n)/3 = b(n) + 48*b(n-1), with b(n) := A089513(n).