A352902 a(0) = 1; a(n) = Sum_{k=0..floor(n/4)} binomial(n+1,4*k+1) * a(k).

1, 2, 3, 4, 7, 18, 49, 120, 264, 544, 1100, 2256, 4736, 10080, 21456, 45312, 94850, 197412, 410134, 852968, 1778382, 3719364, 7806338, 16451280, 34835184, 74164800, 158854536, 342478432, 743432288, 1625079936, 3576582592, 7922065408, 17648409603

Offset

0,2

Comments

Self-convolution of A351971.

Links

Table of n, a(n) for n=0..32.

Formula

G.f. A(x) satisfies: A(x) = A(x^4/(1 - x)^4) / (1 - x)^2.

E.g.f.: d/dx ( exp(x) * Sum_{n>=0} a(n) * x^(4*n+1) / (4*n+1)! ).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 1, 4 k + 1] a[k], {k, 0, Floor[n/4]}]; Table[a[n], {n, 0, 32}]
nmax = 32; A[_] = 1; Do[A[x_] = A[x^4/(1 - x)^4]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A040027, A051163, A351971, A352901.

Sequence in context: A338928 A110705 A139439 * A119330 A373392 A084644

Adjacent sequences: A352899 A352900 A352901 * A352903 A352904 A352905

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2022

Status

approved