A386513
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * binomial(k+4,5) * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 61, 5365, 1529521, 1165598707, 2064316175293, 7646264783133257, 54571471797846058921, 702880914451594090404601, 15486578255494092846454504205, 558260219954065540499622238580509, 31707506930744375037184483066962163261, 2747328696602823034266635550466257234352117
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*binomial(j+4, 5)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386503
E.g.f. A(x) satisfies A(x) = exp(x + x^5*A''''(x)).
Original entry on oeis.org
1, 1, 1, 1, 1, 121, 87841, 221971681, 1493423016961, 22593988839985921, 683468095232158346881, 37898988106295372711276161, 3602374572375663444650415755521, 556397556871212729711470761587498241, 133676738300734051631377763872501373230081, 48173754506706929414138973409107160269088573441
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*sum(k=1, 4, stirling(4, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386504
E.g.f. A(x) satisfies A(x) = exp(x + x^6*A'''''(x)).
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 721, 3638881, 73388931841, 4439222967191041, 671254901566891891201, 223293614016982999277652481, 148555455012284806644741491166721, 183545166980276574090600617506568885761, 396856587856894056179855967245699021196188161, 1430118352830649099320069857966516939680956145171201
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*sum(k=1, 5, stirling(5, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385322
E.g.f. A(x) satisfies A(x) = exp(x + x^2/2 * A'(x)).
Original entry on oeis.org
1, 1, 2, 10, 94, 1386, 29146, 822928, 29927612, 1359897724, 75429391276, 5013317213136, 393252908602720, 35947138247529952, 3787896504780614864, 455830291523748797776, 62132218311858089750416, 9523376536749853754046864, 1630878867943272798422352400, 310238352508716702644975872192
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*j*binomial(i-1, j)*v[j+1]*v[i-j])/2); v;