A325587
G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n * (1+x)^(n*(n+3)).
Original entry on oeis.org
1, 4, 26, 144, 861, 5300, 33974, 226716, 1572134, 11318196, 84460828, 652359324, 5207769776, 42909334344, 364439847976, 3186742207624, 28656418042704, 264722157073936, 2509700822675234, 24395793491141136, 242936835660951240, 2476311278424167804, 25817877582760234776, 275124609022178797944, 2994612410107793787156, 33272066553220515090708, 377127538637173442895684, 4358346743099457288466696
Offset: 0
G.f.: A(x) = 1 + 4*x + 26*x^2 + 144*x^3 + 861*x^4 + 5300*x^5 + 33974*x^6 + 226716*x^7 + 1572134*x^8 + 11318196*x^9 + 84460828*x^10 + 652359324*x^11 + ...
such that
A(x) = 1 + 4*x*(1+x)^4 + 10*x^2*(1+x)^10 + 20*x^3*(1+x)^18 + 35*x^4*(1+x)^28 + 56*x^5*(1+x)^40 + 84*x^6*(1+x)^54 + 120*x^7*(1+x)^70 + 165*x^8*(1+x)^88 + ...
-
{a(n) = my(A = sum(m=0, n, (m+1)*(m+2)*(m+3)/3! * x^m * (1+x +x*O(x^n))^(m*(m+3)) )); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
A325581
G.f.: Sum_{n>=0} (n+1) * x^n * (1+x)^(n*(n+1)).
Original entry on oeis.org
1, 2, 7, 24, 98, 430, 2062, 10610, 58240, 338984, 2081189, 13423258, 90626012, 638509008, 4682120763, 35650040782, 281266115870, 2295142774336, 19338107378888, 167987656339604, 1502475101768767, 13818574571596432, 130542011977462175, 1265358001625542030, 12572822521590475349, 127943980062492526520, 1332336499429857507073, 14186629118985647254622, 154348478009342665050329, 1714707987491310848285920
Offset: 0
G.f.: A(x) = 1 + 2*x + 7*x^2 + 24*x^3 + 98*x^4 + 430*x^5 + 2062*x^6 + 10610*x^7 + 58240*x^8 + 338984*x^9 + 2081189*x^10 + 13423258*x^11 + 90626012*x^12 + ...
such that
A(x) = 1 + 2*x*(1+x)^2 + 3*x^2*(1+x)^6 + 4*x^3*(1+x)^12 + 5*x^4*(1+x)^20 + 6*x^5*(1+x)^30 + 7*x^6*(1+x)^42 + 8*x^7*(1+x)^(56) + 9*x^8*(1+x)^72 + ...
-
{a(n) = my(A = sum(m=0,n, (m+1) * x^m * (1+x +x*O(x^n))^(m*(m+1)) )); polcoeff(A,n)}
for(n=0,30, print1(a(n),", "))
A325586
G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * x^n * (1+x)^(n*(n+2)).
Original entry on oeis.org
1, 3, 15, 67, 336, 1767, 9873, 58221, 360930, 2345469, 15926115, 112702725, 829218143, 6329731749, 50032666719, 408810685879, 3447546750090, 29963861568735, 268051909321565, 2465213070499965, 23282355990573738, 225577403162464915, 2240023319131286013, 22778185448591006709, 236997065442660095669, 2521130509681288754841, 27401150807636634911205, 304071227823781106763523, 3443058535424619400592874
Offset: 0
G.f.: A(x) = 1 + 3*x + 15*x^2 + 67*x^3 + 336*x^4 + 1767*x^5 + 9873*x^6 + 58221*x^7 + 360930*x^8 + 2345469*x^9 + 15926115*x^10 + 112702725*x^11 + ...
such that
A(x) = 1 + 3*x*(1+x)^3 + 6*x^2*(1+x)^8 + 10*x^3*(1+x)^15 + 15*x^4*(1+x)^24 + 21*x^5*(1+x)^35 + 28*x^6*(1+x)^48 + 36*x^7*(1+x)^63 + 45*x^8*(1+x)^80 + ...
-
{a(n) = my(A = sum(m=0, n, (m+1)*(m+2)/2 * x^m * (1+x +x*O(x^n))^(m*(m+2)) )); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
Showing 1-3 of 3 results.
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