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A228339
Fourth differences of Catalan numbers (A000108).
0
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 29 2013
STATUS
approved