A351971 a(0) = 1; a(n) = Sum_{k=0..floor(n/4)} binomial(n,4*k) * a(k).

1, 1, 1, 1, 2, 6, 16, 36, 72, 136, 256, 496, 992, 2016, 4096, 8256, 16513, 32913, 65689, 131785, 266482, 544230, 1124344, 2352188, 4984968, 10699656, 23244976, 51072256, 113370112, 253930816, 573005056, 1300390016, 2962852353, 6766967329, 15472840497

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f. A(x) satisfies: A(x) = A(x^4/(1 - x)^4) / (1 - x).

E.g.f.: exp(x) * Sum_{n>=0} a(n) * x^(4*n) / (4*n)!.

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 4 k] a[k], {k, 0, Floor[n/4]}]; Table[a[n], {n, 0, 34}]
nmax = 34; A[_] = 1; Do[A[x_] = A[x^4/(1 - x)^4]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A027826, A351970, A352066.

Sequence in context: A365079 A038503 A352066 * A365245 A079990 A127902

Adjacent sequences: A351968 A351969 A351970 * A351972 A351973 A351974

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 26 2022

Status

approved