A228339 Fourth differences of Catalan numbers (A000108).

3, 9, 30, 102, 352, 1230, 4344, 15483, 55626, 201246, 732564, 2681223, 9861342, 36428320, 135100620, 502841295, 1877678370, 7032454470, 26410804020, 99437742720, 375260126904, 1419223506516, 5378236459328, 20419260060462, 77659985060772, 295844249258796, 1128738495397128, 4312685074680465, 16500218817839274, 63209983347693924

Offset: 0

Author

N. J. A. Sloane, Aug 29 2013

Keywords

• nonn

Links

• Jocelyn Quaintance and Harris Kwong, A combinatorial interpretation of the Catalan and Bell number difference tables, Integers, 13 (2013), #A29.

Crossrefs

Cf. A000108, A000245, A026012, A033434, A059346.

Programs

Mathematica

Differences[Table[CatalanNumber[n], {n, 0, 30}], 4] (* Amiram Eldar, Jul 10 2023 *)

Formula

From Amiram Eldar, Jul 10 2023: (Start)

a(n) = 9*(9*n^4 + 54*n^3 + 135*n^2 + 122*n + 40) * n! * binomial(2*n, n)/(n+5)!.

Sum_{n>=0} a(n)/4^n = 38. (End)