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).
1, 1, 3, 61, 5365, 1529521, 1165598707, 2064316175293, 7646264783133257, 54571471797846058921, 702880914451594090404601, 15486578255494092846454504205, 558260219954065540499622238580509, 31707506930744375037184483066962163261, 2747328696602823034266635550466257234352117
Offset: 0
Keywords
Programs
-
PARI
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;
Formula
E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..5} binomial(4,k-1) * x^k/k! * (d^k/dx^k A(x)) ).