Original entry on oeis.org
1, 2, 9, 54, 412, 3834, 42131, 533558, 7645065, 122177706, 2153221318, 41464853266, 865908079369, 19484990264956, 469910189792853, 12089047867952058, 330423404118495975, 9561012695542004496
Offset: 1
-
T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] + x^(n+1))^(k+1), x, n-k]]; Table[T[n, 1], {n, 1, 20}] (* G. C. Greubel, Jan 28 2020 *)
Original entry on oeis.org
1, 1, 3, 13, 77, 587, 5484, 60582, 771261, 11102828, 178144861, 3149976426, 60825085447, 1273060083700, 28700081677767, 693217471426114, 17857152401368800, 488620956679818191, 14152040894854881662, 432509671322583878614, 13908794132963653028146
Offset: 0
-
T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] + x^(n+1))^(k+1), x, n-k]]; Table[T[n, 0], {n, 0, 20}] (* G. C. Greubel, Jan 28 2020 *)
A127132
Self-convolution cube-root of column 2 (A127129) of triangle A127126.
Original entry on oeis.org
1, 1, 5, 36, 336, 3793, 49691, 736301, 12130141, 219488417, 4322334090, 91974793971, 2102457339356, 51377007363853, 1336508757460743, 36876168645675673, 1075680625224925835, 33076997985647151025
Offset: 0
-
T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] +x^(n+1))^(k+1), x, n-k]]; CoefficientList[Series[ (Sum[T[n, 2]*x^n, {n,0,22}]/x^2)^(1/3), {x,0,20}], x] (* G. C. Greubel, Jan 28 2020 *)
A127133
Self-convolution 4th root of column 3 (A127130) of triangle A127126.
Original entry on oeis.org
1, 1, 6, 52, 576, 7591, 114365, 1923185, 35541761, 714104502, 15475682769, 359547718332, 8911727170149, 234697278951915, 6544781944957233, 192669771715328227, 5971713743277322517, 194402722591654350978
Offset: 0
-
T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] +x^(n+1))^(k+1), x, n-k]]; CoefficientList[Series[ (Sum[T[n, 3]*x^n, {n,0,25}]/x^3)^(1/4), {x,0,20}], x] (* G. C. Greubel, Jan 28 2020 *)
A127134
Central terms of triangle A127126; a(n) = A127126(2n,n).
Original entry on oeis.org
1, 2, 18, 284, 6680, 211398, 8439235, 407247048, 23056215138, 1498169721930, 109876657252604, 8976437481923520, 808257688877060396, 79516093326076500590, 8485004019719253675540, 976009472808194554659440
Offset: 0
-
T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] +x^(n+1))^(k+1), x, n-k]]; Table[T[2*n, n], {n,0,20}] (* G. C. Greubel, Jan 28 2020 *)
A127135
Derived from the central terms (A127134) of triangle A127126; a(n) = A127126(2n,n)/(n+1).
Original entry on oeis.org
1, 1, 6, 71, 1336, 35233, 1205605, 50905881, 2561801682, 149816972193, 9988787022964, 748036456826960, 62173668375158492, 5679720951862607185, 565666934647950245036, 61000592050512159666215
Offset: 0
-
T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] +x^(n+1))^(k+1), x, n-k]]; Table[T[2*n, n]/(n+1), {n, 0, 20}] (* G. C. Greubel, Jan 28 2020 *)
Showing 1-6 of 6 results.
Comments