A089272 Fourth column (k=5) of array A078739(n,k) ((2,2)- generalized Stirling2) divided by 12.

1, 48, 1412, 34400, 766416, 16296448, 337709632, 6896540160, 139644851456, 2813500878848, 56517475402752, 1133320271749120, 22702062218039296, 454469171469877248, 9094518828981174272, 181952003020274401280

Offset: 0

Author

Wolfdieter Lang, Nov 07 2003

Keywords

• nonn
• easy

Comments

The numerator of the g.f. is the n=2 row polynomial of the triangle A089276.

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, arXiv:quant-ph/0402027, 2004.
• Index entries for linear recurrences with constant coefficients, signature (40, -508, 2304, -2880).

Crossrefs

Cf. A071952, A089271, A089273, A071951 (Legendre-Stirling triangle).

Programs

Mathematica

LinearRecurrence[{40, -508, 2304, -2880}, {1, 48, 1412, 34400}, 16] (* Jean-François Alcover, Feb 28 2020 *) (* Jean-François Alcover, Feb 28 2020 *)

Formula

G.f. (1+8*x)/((1-2*1*x)*(1-3*2*x)*(1-4*3*x)*(1-5*4*x)).

a(n)= (3500*20^n - 3780*12^n + 945*6^n - 35*2^n)/630 = d(n) + 8*d(n-1), with d(n) := A071952(n+4)= (2500*20^n - 2268*12^n + 405*6^n - 7*2^n)/630, n>=1.