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;
A385940
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 5, 148, 17189, 5676336, 4326290857, 6602349049360, 18222895109730537, 84299882148193513600, 616234715187848381357261, 6792153358905298302629935104, 108647409624774384033524243233165, 2443481854821246436998727854436139008, 75225062360951292682727255438183855480625
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+j^3)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385941
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^4) * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 5, 268, 88997, 114813696, 431933720137, 3924557764490560, 75445736579647162857, 2782590090487142758353280, 182621397948270167786531824781, 20092371907364577184989521575079424, 3530551258386563793887714321816262653965, 951815440668013126114976449397609983348430848
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+j^4)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385942
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^5) * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 5, 508, 497861, 2554041696, 47918955042217, 2608995595530944320, 350836859825187730934697, 103472315352121087796983183360, 61101436986101317921145771113951181, 67212924933426575369862458525709786073344, 129898118403746997254471428114728554653243564525
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+j^5)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385943
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^6) * binomial(n-1,k) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 5, 988, 2888933, 59194266336, 5550172939486537, 1812719786900514856960, 1706146365658760367161728617, 4025335006744077207541517795929600, 21392361120121469487882204135345762936461, 235316442953945260569915546964215106936729204224
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+j^6)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.