A376096
a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1)^3 * a(k) * a(n-k-1).
Original entry on oeis.org
1, 1, 9, 260, 17215, 2189997, 477731884, 164858203944, 84745577983095, 61951785517193675, 62077057930391945969, 82749694746019635920952, 143157935882304543684640676, 314805573970543375502985796300, 864458294787075036217714712292600, 2919280453922974335841433174057739408
Offset: 0
-
a[0] = 1; a[n_] := a[n] = Sum[(k + 1)^3 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 15}]
nmax = 15; A[] = 0; Do[A[x] = 1 + x A[x]^2 + 7 x^2 A[x] A'[x] + 6 x^3 A[x] A''[x] + x^4 A[x] A'''[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
A376097
a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1)^4 * a(k) * a(n-k-1).
Original entry on oeis.org
1, 1, 17, 1410, 364019, 228282823, 296324235500, 712075198644414, 2918094100584013255, 19151474626728425949663, 191553141880332262049655201, 2804913258838830873001491036584, 58168297154586087400230338311689652, 1661461159115675581245556180230933084340
Offset: 0
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a[0] = 1; a[n_] := a[n] = Sum[(k + 1)^4 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
nmax = 13; A[] = 0; Do[A[x] = 1 + x A[x]^2 + 15 x^2 A[x] A'[x] + 25 x^3 A[x] A''[x] + 10 x^4 A[x] A'''[x] + x^5 A[x] A''''[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
A376137
a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^k * (k+1)^2 * a(k) * a(n-k-1).
Original entry on oeis.org
1, 1, -3, -34, 495, 13631, -467404, -23984426, 1490938299, 123999435015, -12164649041259, -1497474725212924, 212746558833692052, 36393896155519042476, -7062273474686464802160, -1603475573855830444120802, 407344895625777134555939139, 118552169162473363108837155199, -38177398083353809033748641523305
Offset: 0
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a[0] = 1; a[n_] := a[n] = Sum[(-1)^k (k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[] = 0; Do[A[x] = 1/(1 - x A[-x] + 3 x^2 A'[-x] - x^3 A''[-x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
A376126
a(n) = 1 + Sum_{k=0..n-1} (k+1)^2 * a(k) * a(n-k-1).
Original entry on oeis.org
1, 2, 11, 127, 2446, 69766, 2758136, 144660949, 9742594594, 820936644105, 84720182796109, 10518406503248799, 1547501158599695053, 266325797207877471893, 53021169588315247959918, 12092601263851930181412631, 3132724961425012148414534036, 914922971820526793968713748093
Offset: 0
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a[n_] := a[n] = 1 + Sum[(k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}]
nmax = 17; A[] = 0; Do[A[x] = 1/((1 - x) (1 - x A[x] - 3 x^2 A'[x] - x^3 A''[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Showing 1-4 of 4 results.