A379188
G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^3) * (1 - x*A(x))^3).
Original entry on oeis.org
1, 4, 34, 392, 5271, 77530, 1208602, 19620262, 328167191, 5616065633, 97867738285, 1730732539345, 30981439344096, 560293394484145, 10221582080782452, 187884236846039893, 3476266045318846245, 64690833375603622619, 1210026171180264742927, 22736845507710710652858
Offset: 0
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(4*n+5*k+2, n-k)/(n+3*k+1));
A379209
G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^2) * (1 - x*A(x))).
Original entry on oeis.org
1, 2, 9, 53, 357, 2605, 20041, 160074, 1314821, 11036015, 94242752, 816190963, 7151741597, 63287390223, 564791911903, 5077284164245, 45935201005749, 417928249605123, 3821430547469626, 35098466575407095, 323662850948066340, 2995524340795970120
Offset: 0
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a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(2*n, n-k)/(n+2*k+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 *)
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n+3*k+1, n-k)/(n+3*k+1));
A379283
G.f. A(x) satisfies A(x) = 1/( (1 - x*A(x)^3) * (1 - x*A(x)) )^2.
Original entry on oeis.org
1, 4, 42, 612, 10387, 192312, 3766316, 76716624, 1608691229, 34495221722, 752911467734, 16671973428486, 373609441084507, 8457057155407906, 193087102810266948, 4441320670474030222, 102821800799622552713, 2394063264658388861914, 56025225620739219372819
Offset: 0
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a(n) = 2*sum(k=0, n, binomial(2*n+5*k+2, k)*binomial(3*n+3*k+1, n-k)/(2*n+5*k+2));
Showing 1-4 of 4 results.