A351648 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^5.

1, 1, 1, 6, 22, 69, 224, 819, 3296, 13942, 60941, 276399, 1309207, 6479609, 33377271, 178186018, 983386188, 5604262733, 32955823822, 199771724691, 1246747659198, 8000380516898, 52728354046939, 356593588048023, 2472544614851517, 17563971319301049, 127727505109579581

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Formula

a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n+2,k+4) * a(k).

Mathematica

nmax = 26; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n + 2, k + 4] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]

Crossrefs

Cf. A007476, A045500, A351283, A351437, A351438.

Sequence in context: A247168 A353704 A305032 * A171495 A178706 A276779

Adjacent sequences: A351645 A351646 A351647 * A351649 A351650 A351651

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 16 2022

Status

approved