A007188 Multiplicative encoding of Pascal triangle: Product p(i+1)^C(n,i). (Formerly M1722)

2, 6, 90, 47250, 66852843750, 2806877704512541816406250, 1216935896582703898519354781702537118597533386230468750

Offset

0,1

Comments

n-th power of x+1 using the encoding of polynomials defined in A206284 and A297845. - Peter Munn, Jul 20 2022

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..6.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

N. J. A. Sloane, An on-line version of the Encyclopedia of Integer Sequences, Electronic J. Combinatorics, Vol. 1, no. 1, 1994.

Index entries for triangles and arrays related to Pascal's triangle

Formula

a(0) = 2; for n > 0, a(n) = A297845(a(n-1), 6). - Peter Munn, Jul 20 2022

Mathematica

c[n_] := CoefficientList[(1 + x)^n, x]; f[n_] := Product[Prime[k]^c[n][[k]], {k, 1, Length[c[n]]}]; Table[f[n], {n, 1, 7}] (* Clark Kimberling, Feb 05 2012 *)

Crossrefs

Leftmost column of square array A066117.

Cf. A007318, A123098, A206295, A206284, A267096, A297845.

Sequence in context: A177861 A218151 A343021 * A206156 A229052 A363838

Adjacent sequences: A007185 A007186 A007187 * A007189 A007190 A007191

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved