A346767a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(6*k,k) / (5*k + 1).

1, 1, 7, 70, 855, 11907, 182714, 3029040, 53565875, 1001599339, 19674910572, 404009742858, 8638256718929, 191702754433132, 4403979321915615, 104496256532120370, …

The first 4 terms appear at position 38,135.

…32471107466222850871066611770346535283957762599774467…
position 38,135
termsstringfirst positionoccurrences
11199,997,334
211949,997,964
3117941,000,425
41177038,13510,133
511770855358,593,26711

Searched the first 1,000,000,000 digits. Strings longer than 12 digits are not indexed.