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A336022 a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} Stirling2(n-5,k) * a(k). 2
1, 1, 1, 1, 1, 1, 1, 2, 5, 15, 52, 203, 878, 4172, 21767, 125536, 809254, 5890115, 48560551, 450859572, 4657423009, 52802518648, 649162712358, 8574743501046, 120876064485660, 1809924607067234, 28694297293078915, 480719498205658859, 8502406681853097237 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Shifts left 5 places under Stirling transform.

LINKS

Table of n, a(n) for n=0..28.

FORMULA

E.g.f. A(x) satisfies A(x) = 1 + x + x^2/2 + x^3/6 + x^4/24 + Integral( Integral( Integral( Integral( Integral A(exp(x) - 1) dx) dx) dx) dx) dx.

MATHEMATICA

a[0] = a[1] = a[2] = a[3] = a[4] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 5, k] a[k], {k, 0, n - 5}]; Table[a[n], {n, 0, 28}]

nmax = 28; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + x^3/6 + x^4/24 + Integrate[Integrate[Integrate[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], x], x], x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!

PROG

(PARI) lista(nn) = {my(va = vector(nn, k, 1)); for (n=6, nn, va[n] = sum(k=0, n-5, stirling(n-6, k, 2)*va[k+1]); ); va; } \\ Michel Marcus, Jul 05 2020

CROSSREFS

Cf. A003659, A007469, A336020, A336021.

Sequence in context: A203646 A292935 A000110 * A303924 A336021 A186001

Adjacent sequences:  A336019 A336020 A336021 * A336023 A336024 A336025

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 05 2020

STATUS

approved

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Last modified January 18 12:44 EST 2021. Contains 340254 sequences. (Running on oeis4.)