A386505
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^2 * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 43, 1717, 146261, 22851301, 5923208845, 2370243182889, 1386889039102537, 1137386506152214441, 1263728857603292729441, 1850186029852575829090909, 3487711314718246830637945549, 8300937715895750334611432889933, 24529666348754849148034163067487381
Offset: 0
-
A386505[0] = 1;
A386505[n_] := A386505[n] = If[n==0,
1,
A386505[n-1]+ Sum[(1+k)*k^2*Binomial[n-1,k]*A386505[k]*A386505[n-1-k] ,{k,0,n-1} ]
] ;
Do [ Print[A386505[n]],{n,0,20}] (* R. J. Mathar, Aug 02 2025 *)
-
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^2*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386444
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^3 * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 2, 19, 550, 36314, 4612644, 1005608259, 346940795318, 178328747938574, 130358697631572620, 130619605078238043630, 174116069712361545382300, 301220935342882714418320660, 662385014999576998657776303368, 1818909557774291764795223960949603, 6142458248209027135766781428841480918
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, j^3*v[j+1]*v[i-j])); v;
A386445
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^4 * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 2, 35, 2904, 749262, 469791130, 609789812623, 1465325443822620, 6004904311876287022, 39410188505158004325524, 394180711528456847821432318, 5771988198703021102520933624372, 119699491661363792184803354859998664, 3418976586120192927373434641290957978490
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, j^4*v[j+1]*v[i-j])); v;
A386446
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^5 * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 2, 67, 16414, 16840826, 52661283276, 409599480216723, 6884957718009061046, 225620064835937122627934, 13323090455565480199133495252, 1332335691963961772604470940370302, 214576660211223693770379106296061734124, 53393968668333658608864584261609697870131860
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, j^5*v[j+1]*v[i-j])); v;
A386447
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^6 * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 2, 131, 95760, 392424606, 6132419429842, 286126426174265119, 33663060172069656177612, 8824636572155130972996888814, 4689791333849576329442118802082252, 4689800713441077274969296364554337253614, 8308277421310507219950890075481144453543272228
Offset: 0
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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, j^6*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.