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A351818 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^5) / (1 - x)^5. 4
1, 1, 6, 31, 211, 1841, 18547, 210664, 2682657, 37807531, 581985596, 9696297528, 173702897000, 3327063115248, 67790086866271, 1462900566163696, 33310115601839624, 797687851718024035, 20032231443590167914, 526189230537615409571, 14423255501358439152231 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..452

FORMULA

a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+4*k+3,n-k-1) * a(k).

MATHEMATICA

nmax = 20; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^5]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 4 k + 3, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A000110, A045500, A125274, A351815, A351816, A351817.

Sequence in context: A199320 A097176 A121754 * A200775 A244255 A299550

Adjacent sequences:  A351815 A351816 A351817 * A351819 A351820 A351821

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 20 2022

STATUS

approved

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Last modified October 6 16:34 EDT 2022. Contains 357270 sequences. (Running on oeis4.)