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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

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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)

a(n) ~ 81 * 4^n / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Oct 04 2025

MATHEMATICA