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 *)
Original entry on oeis.org
1, 3, 18, 139, 1314, 14658, 188012, 2721462, 43837014, 777266691, 15037898091, 315177210360, 7112634073455, 171930274269408, 4431595775955999, 121321383915646543, 3515347574087951331, 107474295428549047272
Offset: 2
-
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, 2], {n, 2, 20}] (* G. C. Greubel, Jan 28 2020 *)
A127131
Self-convolution square-root of column 1 (A127128) of triangle A127126.
Original entry on oeis.org
1, 1, 4, 23, 175, 1650, 18451, 237703, 3457763, 55967155, 996755108, 19360232181, 407152004331, 9215091412811, 223307281633261, 5768104533416742, 158197552561322216, 4591028199312877166, 140551293414196198297
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, 1]*x^n, {n,0,22}]/x)^(1/2), {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.
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