A143925
E.g.f. A(x) satisfies A(x) = exp(x + x^2*A'(x)).
Original entry on oeis.org
1, 1, 3, 25, 397, 10061, 369061, 18415825, 1197307161, 98248658905, 9928361978281, 1211474323983221, 175635827999270629, 29845580180227776277, 5876070628821158239293, 1327055145216772464211321, 340793190982323564066166321, 98752652958563191504390390577
Offset: 0
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;
A386506
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^3 * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 79, 8845, 2875301, 2173904341, 3302241027205, 9087841330660905, 41958697476222137161, 306298931820000949752841, 3372659958223293180648888761, 53908617652925799897200239787869, 1211704268213547361986251511514073293, 37286568732242131447316119558759880633085
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^3*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386508
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^5 * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 295, 287917, 1475577461, 27675935977381, 1506650312499716245, 202590228421127415254121, 59748112811137686928254493705, 35281260624146463343889980853779081, 38809774783723742261321649306513968984201, 75004702183951627532765950774478944180316824189
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^5*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386509
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^6 * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 583, 1702357, 34872788861, 3269533221246901, 1067826281292319819285, 1005038096045094314876257929, 2371191405228277266497568590592937, 12601507027818562471139233302156639660841, 138616715922712004054565802733773706346507326441
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^6*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.