A274735
G.f. satisfies A(x) = (1 + x*A(x))^3 * (1 + x*A(x)^2).
Original entry on oeis.org
1, 4, 26, 210, 1901, 18445, 187524, 1971672, 21263360, 233907762, 2614446624, 29607343948, 338977591904, 3917185497535, 45629006313280, 535199773167207, 6315789123860388, 74932400322972992, 893276792585933870, 10694510040508714014, 128531711285410216883, 1550159476645634696615, 18755239991772817629972, 227577929298568261967650, 2768820313297861609739979
Offset: 0
G.f.: A(x) = 1 + 4*x + 26*x^2 + 210*x^3 + 1901*x^4 + 18445*x^5 + 187524*x^6 + 1971672*x^7 + 21263360*x^8 +...
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{a(n) = my(A=1); for(i=1,n, A = (1 + x*A)^3 * (1 + x*A^2) + x*O(x^n) ); polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
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{a(n) = my(A=1); A = (1/x)*serreverse(x*(1-x*(1+x)^3)/(1+x +x^2*O(x^n) )^3 ); polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
A369600
Expansion of (1/x) * Series_Reversion( x * (1/(1+x)^3 - x^3) ).
Original entry on oeis.org
1, 3, 12, 56, 291, 1638, 9780, 60948, 391821, 2577575, 17256918, 117150228, 804343302, 5575177026, 38957753136, 274143594685, 1941037464402, 13818185220783, 98848503602394, 710185896393792, 5122358166219855, 37076879861508830, 269235792063692580
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x)^3-x^3))/x)
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a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(3*n+3*k+3, n-3*k))/(n+1);
A274378
G.f. satisfies A(x) = (1 + x*A(x))^2 * (1 + x^2*A(x)^3).
Original entry on oeis.org
1, 2, 6, 24, 111, 552, 2873, 15458, 85312, 480314, 2747845, 15928080, 93347153, 552181372, 3292571913, 19769887128, 119430685503, 725375643416, 4426786390959, 27131644746326, 166932630227613, 1030684209393288, 6383992918008611, 39657230694169284, 247008096338698523, 1542292860296588558, 9651791500807437834, 60528789932966226468, 380333245334293851637, 2394179659042901060436, 15096873553004201457425
Offset: 0
G.f.: A(x) = 1 + 2*x + 6*x^2 + 24*x^3 + 111*x^4 + 552*x^5 + 2873*x^6 + 15458*x^7 + 85312*x^8 +...
such that A(x) = 1 + 2*x*A(x) + x^2*(A(x)^2 + A(x)^3) + 2*x^3*A(x)^4 + x^4*A(x)^5.
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{a(n) = my(A=1); for(i=1, n, A = (1 + x*A)^2 * (1 + x^2*A^3) + x*O(x^n) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
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{a(n) = my(A=1); A = (1/x)*serreverse(x*(1-x^2*(1+x)^2)/(1+x +x^2*O(x^n) )^2 ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
Showing 1-3 of 3 results.
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