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A336021 a(0) = ... = a(3) = 1; a(n) = Sum_{k=0..n-4} Stirling2(n-4,k) * a(k). 2
1, 1, 1, 1, 1, 1, 2, 5, 15, 52, 204, 902, 4532, 26196, 175320, 1351296, 11819348, 115309534, 1236465988, 14419850138, 181652022376, 2462053028798, 35834756184146, 559816444117400, 9389648056139010, 169166236946379128, 3273760080403458226, 67994123544008546820 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Shifts left 4 places under Stirling transform.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

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

MATHEMATICA

a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 4, k] a[k], {k, 0, n - 4}]; Table[a[n], {n, 0, 27}]

nmax = 27; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + x^3/6 + Integrate[Integrate[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], 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=5, nn, va[n] = sum(k=0, n-4, stirling(n-5, k, 2)*va[k+1]); ); va; } \\ Michel Marcus, Jul 06 2020

CROSSREFS

Cf. A003659, A007469, A336020, A336022.

Sequence in context: A000110 A336022 A303924 * A186001 A134381 A107589

Adjacent sequences:  A336018 A336019 A336020 * A336022 A336023 A336024

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 05 2020

STATUS

approved

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Last modified March 6 04:10 EST 2021. Contains 341841 sequences. (Running on oeis4.)