A369617
Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^3 + x) ).
Original entry on oeis.org
1, 4, 22, 146, 1079, 8525, 70468, 601816, 5268241, 47019566, 426250277, 3914020148, 36328457669, 340278596273, 3212416054283, 30534649412247, 291981031204917, 2806832429353512, 27109863184695640, 262951127248539898, 2560229132085602215
Offset: 0
-
A369617 := proc(n)
add(binomial(n+1,k) * binomial(4*n-4*k+2,n-k),k=0..n) ;
%/(n+1) ;
end proc;
seq(A369617(n),n=0..70) ; # R. J. Mathar, Jan 28 2024
-
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)^3+x))/x)
-
a(n) = sum(k=0, n, binomial(n+1, k)*binomial(4*n-4*k+2, n-k))/(n+1);
A379186
G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^3) * (1 - x*A(x))^2).
Original entry on oeis.org
1, 3, 21, 202, 2270, 27903, 363412, 4927840, 68834941, 983680783, 14312988289, 211329419670, 3158263216267, 47682769300288, 726188701482730, 11142842570134264, 172101193009427174, 2673445730846829604, 41742159037922167264, 654721526817143247304, 10311337739352708700427
Offset: 0
-
terms = 21; A[] = 0; Do[A[x] = 1/((1-x*A[x]^3)*(1 -x*A[x])^2) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jun 14 2025 *)
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n+3*k+1, n-k)/(n+3*k+1));
A370844
Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^4 + x) ).
Original entry on oeis.org
1, 5, 35, 295, 2760, 27556, 287564, 3098780, 34216020, 385106280, 4401850866, 50957904938, 596231618166, 7039674475190, 83767631913840, 1003564049999916, 12094813260406732, 146534778450346908, 1783695235540931924, 21803615393276536720, 267537602528379374851
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)^4+x))/x)
-
a(n) = sum(k=0, n, binomial(n, k)*binomial(5*k+3, k)/(k+1));
A379185
G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^2) * (1 - x*A(x))^2).
Original entry on oeis.org
1, 3, 18, 139, 1222, 11618, 116372, 1209779, 12930966, 141225530, 1569136588, 17680779230, 201562070356, 2320574126216, 26942875644408, 315109464849603, 3708926665685286, 43901133108206978, 522240410257549260, 6240258006163094026, 74864641626913850964
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(3*n+k+1, n-k)/(n+2*k+1));
Showing 1-4 of 4 results.