A379189
G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^3) * (1 - x*A(x))).
Original entry on oeis.org
1, 2, 11, 84, 749, 7297, 75263, 807795, 8928259, 100930845, 1161556834, 13563086118, 160286280443, 1913502807883, 23041637546674, 279535792627983, 3413404764685607, 41920395344282046, 517450364496878615, 6416254102356745484, 79884728250064030602, 998261210034672052421
Offset: 0
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n+k, n-k)/(n+3*k+1));
A379191
G.f. A(x) satisfies A(x) = (1 + x*A(x))^3/(1 - x*A(x)^3).
Original entry on oeis.org
1, 4, 31, 338, 4356, 61603, 923958, 14433315, 232298914, 3825260332, 64140203645, 1091364139213, 18796605318655, 327056343952311, 5740466392321499, 101516213938082457, 1807045676161156515, 32352346658163940698, 582185299986049977601, 10524395285312191583304, 191034444423571726099486
Offset: 0
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n+6*k+3, n-k)/(n+3*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));
A379190
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x*A(x))^3.
Original entry on oeis.org
1, 4, 30, 304, 3557, 45150, 604222, 8393282, 119872890, 1749183075, 25964512607, 390828464403, 5951561595889, 91523131078999, 1419293428538496, 22169968253466467, 348507676062911520, 5509187208564734328, 87522347516801353980, 1396619714730284551913, 22375420057050167868366
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(3*n+6*k+3, n-k)/(n+2*k+1));
A379187
G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^2) * (1 - x*A(x))^3).
Original entry on oeis.org
1, 4, 30, 286, 3091, 36063, 442898, 5642628, 73893561, 988585443, 13453580815, 185661101085, 2592069904059, 36545520229810, 519601325300487, 7441580996167052, 107255985242888943, 1554576968046707916, 22644622298400113411, 331322620547205661043
Offset: 0
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a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(4*n+2*k+2, n-k)/(n+2*k+1));
Showing 1-5 of 5 results.