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

0,1

Links

Table of n, a(n) for n=0..29.

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

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)

Mathematica

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

Crossrefs

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

Sequence in context: A096222 A148947 A090573 * A257641 A048119 A304823

Adjacent sequences: A228336 A228337 A228338 * A228340 A228341 A228342

Keyword

nonn

Author

N. J. A. Sloane, Aug 29 2013

Status

approved