A381983
E.g.f. A(x) satisfies A(x) = exp(x) * C(x*A(x)^2), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
Original entry on oeis.org
1, 2, 15, 280, 8365, 342566, 17839339, 1128217084, 83987669721, 7194842276842, 697216089189511, 75408952092397760, 9005278056681754885, 1176889697125038323662, 167076740069554538243427, 25603739419854491589361636, 4212587964283017439802066353, 740650326150658335888643004498
Offset: 0
A349639
a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^k.
Original entry on oeis.org
1, 2, 11, 163, 4177, 150606, 7002679, 399296682, 26997867705, 2112814307980, 187919721166951, 18727570061711897, 2067435790679136937, 250474099952311886236, 33043529154916822685459, 4715582224589290429430011, 723854564711343436767660481, 118933484485939500023357177356
Offset: 0
-
Table[1+Sum[Binomial[n, j]*CatalanNumber[j]*j^j, {j, 1, n}], {n, 0, 20}]
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a(n) = sum(k=0, n, binomial(n,k) * (binomial(2*k,k)/(k+1)) * k^k); \\ Michel Marcus, Nov 23 2021
A381982
E.g.f. A(x) satisfies A(x) = exp(x) * C(x*A(x)), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
Original entry on oeis.org
1, 2, 11, 139, 2829, 78981, 2802163, 120667667, 6113752025, 356342305465, 23488872131871, 1727770084512495, 140302645206245701, 12466960491079733237, 1203253101643330233707, 125351056198801059896491, 14019427299278115378992049, 1675439381194882102492648305
Offset: 0
Showing 1-3 of 3 results.