A367201 -id:A367201 - cp's OEIS frontend

A367199 E.g.f. satisfies A(x) = (1 + x*A(x))^(A(x)^3).

1, 1, 8, 141, 3852, 143460, 6780642, 388851960, 26235133992, 2036243259648, 178742696099040, 17509589369568648, 1893647907646728120, 224106838102512869400, 28809018473999642686584, 3997516614926297143604760, 595518793080901690966354368

Offset: 0

Seiichi Manyama, Nov 10 2023

nonn

Cf. A349505, A367157.
Cf. A162655, A162656.
Cf. A367200, A367201.

a(n) = sum(k=0, n, (n+3*k+1)^(k-1)*stirling(n, k, 1));

a(n) = Sum_{k=0..n} (n+3*k+1)^(k-1) * Stirling1(n,k).

A367200 E.g.f. satisfies A(x) = 1/(1 - x*A(x))^(A(x)^3).

Original entry on oeis.org

1, 1, 10, 201, 6216, 261300, 13923762, 899679144, 68368215528, 5975493315264, 590584798045440, 65132133511182408, 7929604511136220536, 1056369806709005923992, 152854816585283562807288, 23873492748049623945947160, 4002988479012229417182249408

Offset: 0

Seiichi Manyama, Nov 10 2023

nonn

Cf. A264408, A367160.
Cf. A349556, A355766.
Cf. A367199, A367201.

a(n) = sum(k=0, n, (n+3*k+1)^(k-1)*abs(stirling(n, k, 1)));

a(n) = Sum_{k=0..n} (n+3*k+1)^(k-1) * |Stirling1(n,k)|.

cp's OEIS Frontend

A367199 E.g.f. satisfies A(x) = (1 + x*A(x))^(A(x)^3).

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