editing

approved

allocated for Paul D. Hanna

G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n * (1+x)^(n*(n+3)).

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

0,2

Equals column 3 of triangle A325580.

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 + ...

(PARI) {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), ", "))

allocated

nonn

Paul D. Hanna, May 11 2019

approved

editing

allocated for Paul D. Hanna

allocated

approved